I am not a big fan of house rules, since this is supposed to be a balanced game that is played in tournaments, and only loosely based on a WWII theme. But if you insist to add all this extra spice, I suggest to keep it inside the A&A box of known game mechanics. Let China be the base of what happens when your capital is lost. And skip the pro neutral thing, its either true neutral or not neutral.
1. When your capital is lost, all territories under your control become true neutral. You are no longer an active player. You can no longer move any of your former units, they are stuck where you left them last turn. Your ships will not make a seazone hostile. Former allied units on your territory must either combat move out next turn or trigger combat. If you have units in former allied territories, they are removed from the map.
A lot of evidence from the real WWII support this rule suggestion. When the French capital was captured, all other French territories became neutral. Not pro but true. US and UK had to combat move into neutral French Morocco, Germany had to combat move into Vichy, and Japan had to combat move into FIC. Also, all French units that were in UK when Paris fell, were demobilized and sent home to occupied France. When the Italian capitol was taken, the former allied German units in Northern Italy would face combat against the by now neutral Italian units in that territory. When the Finnish capital was taken by Russia in sept 1944, Finland was declared neutral and the former allied German units in Northern Finland faced combat against the Finnish forces there. Same with Romania in 1944. And so on. When Japan captured the Chinese capital Bejing in 1937, China become neutral. When this game start, China is a neutral with an occupied capitol.
2. When a neutral territory is attacked, it is no longer neutral but allied to the enemy of the attacker. And remember, with this rule there are no pro neutral, only true neutral, so a combat move into a neutral territory will never trigger a world wide uprising by other neutrals, like in the OOB rules.
Evidence to support this.
Neutral Poland is attacked by Germany and Russia and get allied to UK and France. No other true neutral join the war.
Viborg territory of neutral Finland is attacked by Russia, and can join the Western Allies, but the road to Finland is blocked by other neutrals that dont want to join the war.
Neutral countries Norway, Denmark, Belgium and the Netherlands is attacked by Germany, and taken in one round since they are one territory each. No other true neutrals join the war.
3. When a neutral nation is at war, and it has no capitol, either because the capitol was taken in a previous turn, or it is a minor one territory nation, or Mongolia, then it can purchase infantry only, limited by its income, and place this infantry in any territory in order to the Chinese special OOB rule