Would set days be possible?

Yes. You would need to set aside perhaps a full week for orientation. Call some agencies and explore your options! It is a bit unusual to work less than 36 hours so it will be harder to find a good fit for you. The process will likely be that agencies will contact hospitals with existing needs (you can help sort out hospital locations that will work for you first) and see if they are willing to take you for just 24 hours a week. Lots of needs out there so again, I think the short answer is yes.

On the down side, there will be some tax issues requiring a consult (usually free) with an expert such as TravelTax. A good bit of travel compensation comes in the form of tax free stipends for housing and per diems. The work-around for housing is that if you take full time housing at your assignment, that stipend would be fully non-taxable. A housemate situation could cover that but your agreement would have to be full access all month. If you choose something like a motel a night or two a week, your housing stipend would have to be prorated. You would definitely owe taxes on most of your per diems ("every or per day" is the English translation) and that definitely would require a tax pro. The travel stipend would be fully non-taxable reimbursement, for one round trip (not weekly). Tax rules have changed and I'm not sure you would be able to deduct your weekly round trips by itemizing on your tax return. In any event, that would also require a tax expert's advice. Do not use your current tax preparer if you have one, you need a specialist in travel taxes.

If you are planning on finding something close enough to commute to, there is another set of issues. First, all your compensation must be taxed and travel companies are reluctant to do that. If they go the normal route with stipends, you are free to claim that as extra income at the end of the year. That works for the first year, after that the IRS may propose that you file estimated taxes quarterly or even more frequently (a tax professional makes that easy though). Second, local hospitals usually do not allow local travelers. And in fact, if this is your plan, you are probably better off simply signing on as per diem at a localish hospital.

Finally, see if your hospital will allow you to work extra days. Overtime pay may or may not match what you can do on the free market, but if allowed would be a lot less hassle, and you could perhaps ramp it up and down to fit your needs rather than an inflexible contract.

Similar question for any travelers- how willing are department managers to give you block scheduling or consecutive shifts? I am wanting to do somewhat local travel and do either 3-12s or 4-10s in a row (Cath lab/IR is my field), so I can still come home on weekends. Anyone else run into issues with this in the past?

That is a common request, and up to manager's discretion and needs. Any such agreement should be inshrined and spelled out in your contract or it is worthless.