Absolutely FANTASTIC idea! But keep it simple.
Move the strats to the rear, but not all clustered around the protected bases (or else all we'll see is Me163s which afterall were only used minimally in RL). Besides we now have the uber-Jug which will do 40k.
Make the strats bigger -- maybe 2x or 3x -- requiring more than one or two flights to shut them down. Perhaps several of a given type of strat (say refineries) in a given geographic region, such as the ball-bearing factories in or around Schweinfurt in RL.
Give the strats' destruction a bigger impact on base replenishment, i.e. scarcity of the product across the country. Perhaps limiting the resupply between bases to to a fraction now capable as a factor of the strat percentage. Possibly by requiring more C47 or M3 trips to accomplish the task than when the strat is at full production, or by reducing inventories at the base providing the resupply. For instance, reconstituting troops at A1 from V2 would mean that for every barracks the pops back up at A1, one is lost at V2. And a country's training facility could resupply all troops (i.e. pop up all barracks) in one hour at 100%, two hours at 50%, etc. Likewise with refineries, ammo factories, radar, and so on.
Make it harder or require more effort to resupply or rebuild a strat to a point that makes it more viable to defend the strat in the first place than just resupply it afterwards, instead of the current instance where, rather than defend the HQ from a bomb raid, pilots up C47s and M3s to re-establish the HQ within five minutes after a successful bomber strike rather than fly up to attack the bombers, thereby nullifying the the attacking country's stategic effort.
Anyway, I love the idea of enhancing the strategic side of the game and was just spitballing some ideas.