I agree that advanced start modern age is pretty good. I guess you can either argue that production/gold at advanced start tend to be low enough to create an artificial constraint, or that it's proof the snowball is too much.
I think we're approaching this from two different viewpoints, with different priorities.
My priority is making victory feel more satisfying. I think that there's a fundamental issue with having a normal gameplay loop in an age where you are racing to victory. I.e. the standard gameplay loop and the victory race are in opposition to one another. In a victory race, the goal - especially on higher difficulty or in multiplayer - will be to doggedly pursue your chosen victory type. That means you won't really explore the features of your chosen civ unless they help boost the way you are trying to win. That in turn skews the designs of those civs if they are to be relevant. The snowball also gets pretty extreme, and adds to the feeling that your chosen civ seems to really not matter. Making modern era work like other eras - where you are trying to score points rather than a race I think is a good idea, and would really help let those civs shine. But, score victory probably isn't very satisfying for a lot of players, it is kind of an "oh, the game ended" kind of moment.
To that extent the idea of a short 4th "victory race" age, which doesn't try to introduce new civs, and which just pools together the accumulated bonuses you've acquired, feels like an interesting way to make an ending actually feels definitive. At the same time, it allows the current modern era civs to go through a full game loop. What I really wouldn't like in a 4th age is for Firaxis to just shift the problems which are currently there in the 3rd age, one step further along the chain. That would to my mind devalue any new civs who were introduced.
I get the impression that your priority would be a full age where we'd get to experience cold war/globalization/WW2 etc, with a roster of contemporary civs? So I can appreciate that a short "victory age" would feel like you were being cheated out of something cool.
That's perfectly valid, but to me, just adding an age without solving existing problems still leaves the question of how to make victory satisfying still up in the air. It still leaves questions around how to make civs matter in an age which is a victory race, how to mitigate a 3rd snowball cycle when 2 is already a lot, and - for me - the micromanagement at the end of age 3 is approaching the limit of what I want to see, how to keep that under control? Plus, the civ roster already feels very sparse and repetitive with only 11 civs per age, I really don't want to see a new age's worth of civs until we've at least doubled the current civ count.
And I guess you could always combine the two viewpoints and have a 5th mini-victory age after the modern era (or an era of your choice).
Gold and production were somewhat of a constraint, but I feel the main conclusion I got from my advanced start game was that it made me have to setup my empire before I was able to pursue a victory.
Antiquity has founding your first cities to get your first resources and yields before you try to win, Exploration has settling in distant lands and setting up your religion treasure resources and building adjacencies before you try to win, but Modern has no setup beyond what is necessary for victory. Archeology doesnt feed into your larger empire, Ideologies offer some nice bonuses but can be ignored if you dont care about the military victory, factories come in way too late to matter, and the entire tech tree funnels you solely into rocketry and the science victory rather than letting you specialize. Heck, the Age even starts with oil rigs and rubber already improved despite oil drilling not becoming a thing until the mid 1800s.
It's not merely a problem with snowballing, but the entire age feeling like its jumpstarted to put you into a victory race rather than letting you build a modern empire. This is why I strongly disagree with people wanting a Victory race 4th age since we already have one.
Some things I feel could be changed to have a normal civ gameplay loop balanced with the victory race at the end would be to:
1) Emphasize the importance discovering and developing coal, oil, and rubber for the this Age
Make it so that they start off unimproved so that you would still need to settle more lands or switch your towns to grow instead of being specialized which will cut down on the initial income spike and make people focus on developing their empires. Coal, Oil, and Rubber will have more effects rather than just increasing combat strength. There could also be unique improvements unlocked in the tech tree that you would have to build or buy in order to properly hook up the resource and increase its yields and act as another gold/production sink to mitigate snowballing. It might be even better to turn them into factory resources that dont contribute to the economic victory since those apply empire wide bonuses which leads me to the next change.
2) Unlock factories before rail connections
The way factories are set up means that they come in extremely late and are really only useful for an economic victory rather than being an important part of your empire. Unlocking factories sooner makes them and factory resources a more vital part of your empire building so you can feel the bonuses they provide rather than just using them for Economic Legacy points. Rail connections would still be important though since only settlements connected by rail will contribute points thus letting you be a bit more strategic in setting up a victory point factory versus a production factory. This way, factory resources become a vital part of your empire development rather than just a legacy path.
3) Widen the tech tree
Something I've said numerous times already but I cant state enough is how the tech tree in all ages feels more like a funnel than branches. Making the tree have even just one or two extra branch per tier would open up space for a lot of new techs and potential for specializing your empire. Certain techs could be moved to lower tiers on separate branches and higher tiers could be filled out with atomic and information age techs. For making the start of the age feel more in line with the others by having a "setup" phase though, having maybe 5 techs to choose from at the start of the age, all with masteries and connected techs that could specialize your empire in different ways, would fulfill this and mitigate snowballing somewhat simply by introducing more things to sink beakers into.
I think with these changes, they could give the Modern Age the distinct phases that it lacks: first a setup phase where you are solidifying control over valuable factort resources through growth, conquest, and trade, second an ideological conflict phase which is basically the current modern age but now everybody has setup their empires to be specialized in different ways both technologically and culturally, and finally the victory race phase which emphasizes strengths of the modern empire you have built while having techs and civics that amplify them rather than just providing more buildables. (Maybe make the GDR a future tech unlock though)