HN cavalry (either from Captured upgraded Elephants or from Esus-Scouts turned horsemen + masked before upgrading, 2-3 will suffice.

) + into the mist
=
pure solid win in form of tons of gold + economic meltdown for your neighbors in one handy package (and the Workers + Settlers you already built henceforth are safe from a multitude of threats they might have to deal with otherwise) at least in singleplayer or coop-multiplayer (if just Hawks weren't so utterly broken...).

Just avoid those pesky Empyrean light-heads (edit: pun of course intended in a multitude of ways.

) near you...
If done lategame you usually should at least have some possibility to get rid of it (by using various Items like healing salves to pass from one unit to another, which counts as using a spell and thus un-hides them as far as i am informed.
Spellcasters get out there cheap as well at the click of a button...) but its better if you can set up the first mentioned feat early to midgame (if into the mist has any real issue imo, it is the lesser usability in lategame as compared to most other Worldspells which grow more powerful with time.).
Also if you have an Empyrean neighbor you can position the units you want revealed there, their priests will take care of the rest...
And you should be able to exactly set up all those methods to your utmost ability since you have full control of when to trigger the worldspell...
Also Sidar are a decent Civ in their own right and don't need an all-powerful worldspell to hand them further power. Its still far from the worst Worldspell vs. AI if used right. (Its not that i would hate them getting the ability to un-hide at a moments notice. I just don't think its really needed, given that there are other ways around it and in early to midgame it shouldn't be a really big issue... Nox Nocturnis is another issue where un-hiding would make an allready powerful if management-intensive feature downright broken.)
And yes, as Sidar you should have tons! of units to "spare" (Level 3+ out of the box on top of that.).
All those "spare-units" are potential shade material, and thus bad to actually not! have around.
By late midgame or later neither Production nor Upkeep (or heaps of Gold for that matter) should be an issue for you, or something runs not so well anyways (at least Horse-Archers and Champions should be built a turn each in speeds down to epic in your production centers.
Possibly even National Units in places with the Heroic Epic and the likes. Throw in a heap of mercenaries from the GoN or some slaves turned Lunatics (even though that ceased to be very interesting with the new enraged, i must confess) and you are set for some sneaky crunching...).
+ you can continue building more nonhidden units after you cast the spell (and those in cities are seen anyways so city-defense is hardly an issue.). Not all that hard to do with Sidar in lategame.
Getting GoN as a cure for your defensive needs might be the most elegant solution though. In terms of convenience and power. Also not the hardest thing to get usually, given that Sidar are rather hard to beat at building mid-game wonders they want to build. For a multitude of reasons... (and in addition to buying a mercenary for defending the countryside the buying unit should lose its hidden status as well since to my knowledge its a "spell" as well and can join the defensive fun.)
Slave trade from Undercouncil might come a close second here given that its cheaper and possibly the easier way to unhide units en-masse with a similarly useful benefit (but CoE+Overcouncil is more interesting for Sidar by quite a margin in my book, so ill stick to the GoN personally...)
One thing has to be said though, again. It totally sucks in competitive multiplayer for sure (at least if your oponents know how to make it useless). And Birds seriously need a nerf + diversification...