largely similar to how it looks now, i think the layout is actually not terrible, its a bit regionalised early which is a bit of an issue but geographically i think HL/LL needs to remain, I would overhaul the promotion/relegation process.
Feeder leagues would need reorganised but thats a long-term job.
Promotion wise, I'd have one promotion slot each in HL/LL, & feeder leagues
one playoff promotion slot in each.
Relegation wise, bottom four, drop to their respective leagues [HL/LL]
remaining promotion relegation would be okay.
In terms of breaking the old firm domination, i think the only way is to change the co-efficient spots, its the european money that makes the old firm unreachable by the remaining teams in the prem, perhaps an exclusion from the scottish cup would be best for those two teams just until the scales are balanced.
Once the european money begins to dry up/go to other teams (e.g. dundee, motherwell, st mirren) that gives them opportunities to challenge for the title.
unfortunately its all academic unfortunately, in Glasgow youre either green or blue and ultimately that'll never change. but i think fixing the league system is an easier step change to create more competitiveness.
EDIT: to answer your questions; a transfer cap, wage cap would, in my opinion, simply drive clubs into administration, The large Japanese contingent at Celtic for instance brings a lot of ticket sales and merchandise sales, in my opinion it would prevent obtaining these "celebrity" players etc.