Looking for some regulator troubleshooting and advice on buying replacements

I suggest that you keep Scubapro as one possibilty.
The Mk17 evo is sealed diaphragm and the hose position is optimized for two regs on a twin set, without the hassle of a swivel. Two of them are way less than 1000 bucks, if you buy on Ebay:
RO1 01 Scubapro Erogatore MK17 Evo G260 DIN300 + bag erogatore | eBay
If instead you want to switch to piston, the MK25 is a bit more expensive (400 € instead of 360 €) but still inside your budget: RO1 00 Scubapro Erogatore MK25 Evo G260 DIN300 | eBay

 

Most commonly cracking pressure causes this. You have to set it up to match your ip.

 

To your first question, it sounds like there might be IP creep in your OMS regs. It would be a good idea for you to get a basic understanding of how all regulators work if you don't now have that. The first stage has a valve that closes automatically when pressure inside the reg (from the tank) builds to IP (intermediate pressure). Basically it's the 1st stage's job to stop the high pressure air from the tank and only release it to the 2nd stage at a much lower set pressure, which is IP. If this valve starts to leak, which is common, the air pressure going to the 2nd stage begins to 'creep' up and that causes free flows.

You should know that OMS generally has (or has had, I don't keep up with it) a terrible reputation for customer service and quality in the technical diving world. They certainly do not manufacture their regs, they must be re-branded from some other company. It might be interesting to find out what your OMS regs really are.

To your 2nd question, if you are looking for sealed piston regs, Atomic might be your best bet. They're excellent and the company has a very good reputation for customer service. The less expensive models are perfectly fine. But if your main concern is sealed 1st stages, you have more options with diaphragm regulators. I'm not sure you need sealed regs for water in the 50s. 30s and very low 40s, sure, but good technique in water in the 50s should definitely prevent any icing.