I've been with an insurance company in CT, since I started my rental portfolio, but am looking for other options as it seems their rates have been going up and up. 

TurboTenant, you just shrank you the property options pool for your money making prospective tenant pool. 

My other option that i am considering is doing a new construction on a 4plex.

You are absolute spot on when you say @Jonathan Pflueger should win an award that explanation was incredible, concise and very informative and powerful. 

Your situation is probably better for seeking out "Non-QM Lenders" or potentially other "Creative Financing" options

We intend to give them the option of moving out or new contract (increased rent to match the market).

It depends on how much capital you have but I recommend either house hacking (3.5% - 5% down) a 2-4 unit property or you'll need 20-25% down for a non-owner occupant purchase which comes with higher rates.I would say house hacking is not an option for me, because I have a family with 2 kids (need good schools). 

The other option is to go into commercial, for example, warehouses.

The only options that I see are rent by the room, mid term, short term, or just putting more money down.

I'm aware of seller financing as a possible option and will be on the lookout, but it certainly dramatically lowers my deal pool in an already incredibly competitive market.