I haven't actually gone through and figured out the absolute latest you can start saving for all the troops
If you only want to get to the hovers you probably don't need to have saved any techs prior to Indy at all.
If you've pushed ahead on the Indy map in Colonial, all you need to do is get up to Trench Fever as soon as you can, then use the researches on the Indy tree, advancing you to Boarding Houses & Law and Order, while getting you to the Peace Conference story quest. That requires the Police Stations and optionally a residential research - hence not doing Boarding Houses first.
[If you want to do the Indy bonus questline, you should have reached Enemy Propaganda, which requires a cultural research, while there's still a cultural research left to do in Indy. I tend to do most of the questline on aging up into Indy. Researching Modern Roads later, will let you finish it. ]
If you only took the necessary researches on the tree, you will have 8 Indy researches left. Reconaissance can be used to get the armoured car in Progressive. Modern Roads can be used to get the Long-lived Man in Modern and free up the bonus questline.
You need three tech researches in Postmodern (excluding the two at the end which we skip), and two in Future to reach the hovers. That leaves 1 over to get you to the end of the Future Era. You need 9 stored researches to complete AF and OF (as far as the blocker). That's the minimum number you need to have saved up to get the maximum number of troops.
Colonial 2 saveable researches: Porcelain & Industrial Goods
LMA 4: Metal Working, Aristocracy, Pest Control & Optics
HMA 7: Quality products to Water Wheels
So the answer is you can start saving a little way into the HMA tree and still get maximum Higher Age troops in Indy.
