Wp sir! Did you use proxy wars at the beginning or how did you managed to get immigrants throughout the whole game?
Yes, but you dont need to, is just you wont receive as much immigration.
As for your analysis is spot on and i think you realized how important is domestic demand and how bad is to subside.
When you subside you are spending a lot of cash on unprofitable low demand industries to starve your craftsman and decrease demand even further. Than you have to raise tax to keep subsiding and decrease demand even more on all your pops.
Its a bad economic vicious cycle.
Instead of subsiding, try to low your taxes, spend more on military supply (if you have a military industry) and give money to your pops through social reforms (thats why i said unemployed subsides and pensions are good). That will expand demand and your industry will be profitable again which in turn will expand demand even further since your capis and craftsmand will now have money.
Thats a good economic cycle.
Eventually though, your industry will expand too much and require more and more inputs, thats where imperialism will kick in and you will need a lot of colonies to feed your industries with rare raw material (coal, iron, rubber and oil mainly).
As for timber: Its used as input on paper, furniture and lumber, so they may have a profitable industry that is buying it domestically. Its also used on railroads and naval bases.
As a side note: i really feel that country stockpile should have the option to buy only for local producers, that would be a way to make a "good" subside of your productions and realistically emulate the government spending money to heat up the economy. The actual mechanics of subside are a trap that non experienced players will have to learn a way around it and only the most powerful nations of the game can use it scotch free.