Yeah, I've done Deity difficulty no problem.
GAMERTAG: DJ Splendid.
I've got myself a nice save where I'm set up and can pick which victory to go for. I had time last night to finish the game with cultural and economic victories. I'll bag the others at the weekend.
I'm a bit disappointed how easy it was, actually. Last night was my second night playing CivRev. The night before I beat it on King all four ways. I've not played a civ game since Alpha Centauri (fantastic game) but I remember things being a lot harder.
Basic details of what I did:
-Strategised around building a powerful core city on the front line of land-based attack which is grown faster by using settlers from other, inner, expendable cities ('population pumps'

). These settlers are easier to generate with Republic tech, hence chosing Roman. The city was the core of all research or gold, allowing you to go either way and achieve all four victory types [from a solid save game at about 1400AD].
-Saved a game right at spawn and spent a few turns exploring the map to see if it was a good, defensible position to play on Diety with. Things to look for include: advantageous choke points; potential for a defensive line of 'war' cities which block all land routes to your territory; space behind your front line for a grid of pop-pump cities; opportunity for placement of 'culture-buffers' in front of your desired territory (expendable, easily re-takable cities which soak up enemy culture attack); locations of barbarians (essential early gold boost); potential for water-based vulnerability (ideally you'd like to back onto an ice cap with few, thin water routes that can easily be defended; local Civs (if it's France of Egypt then enemy culture will assault you early on) [in fact France was right next to me and I had a HARD fight to annex it and Wall my nearest city off]; aaand other stuff I can't remember.
-Actually drew a rough map of the area together with THOROUGH plans for initial builds and troop movement.
-Reloaded the spawn save I was happy with [as it happened, it was the first I tried!]
-Stuck to ze plan.
-Saved in a very careful, organised manner. I had five 'phase' saves - big jumps of progress at very secure times - and a bunch of spammy 'just in case' ones.
-Stuck to ze plan.
-Maximised variables at all times, ie, spammed roads, never used rally points or multi-turn move orders, kept things in flux and moving around. Mobility is the #1 defence as you're hugely outnumbered. The CPU will reeaallly want to kill you. When you find yourself having to load a game to deal with / mitigate an unforeseen, critical threat you want as many variables as possible to play with. Unit sacrifice / damage limitation - even random flukes like finding the Cities Of Gold on the turn RIGHT before your city flips to France which gives you enough cash to finish your wall - can be 'pushed for' by simply keeping your options open. Fortune favours the WORKING YOUR ASS OFF
-Stuck to ze plan.
-Made careful use of combat units. When dealing with CRITICAL combat, I'd save the game then attempt my desired action. If a 30>4.5 attack randomly went awry, rather than kicking my TV, I'd reload then carry out combat action elsewhere with insignificant units. This takes advantage of the 'preserved random seed' used internally by the game. Effectively, you use up a bad dice roll elsewhere, and you go back to where you're concerned about with more 'nominal' dice rolls.
In total, definitively did not reload more than 15 times from start to victory for both Cultural and Economic victories between start and 1750AD.
Not bad considering that I took until 1950AD on King
Good luck!