@David Sisson, just a few thoughts.
1550 sounds a high to me but I don't know the property or area. That 2nd bathroom does help. If it's a big unit then that might be OK.
You can usually tell whether you're asking too much by the volume of calls you're getting. If you aren't getting a lot of calls, you're high/reaching. If the phone's ringing off the hook then you might be under market. A manageable level of calls usually means you're in the market zone.
However with all your extra terms (pet rent, having tenants pay water), I would be clear about that in the listing so tenants know what the true price is and can use that in deciding whether to call.
Additional pet RENT is fine, but an additional pet or cleaning deposit, if it puts the total collected deposit over one month's rent, is illegal in Rhode Island AFAIK (check with your attorney - I am not one).
I was told, by an attorney, that if you're going to have tenants shovel snow and mow the lawn, in order to protect yourself you need to compensate them in some way - whether that's a check or a reduced rent, which is detailed in the lease. Check with your own attorney of course.
And remember, regardless of whether you delegate shoveling and mowing to tenants, at the end of the day you are still the property owner and still the one responsible to make sure it gets done. If it's not done, the city is going to issue you a violation and saying the tenants were supposed to do it is not going to be a valid defense. (Nor do I think you could legally try to pass on such fines to the tenant, but again check with your attorney.)
As far as water goes, it's a similar situation. As landlord, you are responsible to make sure that running water and working sewers are available at all times, that's part of the "implied warranty of habitability". So, you can try to pass such bills on to the tenant, but it's a little toothless - in Rhode Island you are responsible for those bills to be paid, and those services to remain on.
If you still want to do that, which is fine, I would recommend that YOU get the bill and either pay it yourself & get reimbursement, or have the tenant pay it but check that account every month to make sure they did. A middle ground would be that they send the check made out to the water company back to you, then you use their check to pay the company.
If you go that route, I would recommend your lease states that any funds received from the tenant first get applied to late fees, utility bills including water, bounced check fees, etc. and only lastly for rent.
The reason for this is that my understanding is you can only evict for unpaid RENT in Rhode Island, not unpaid late fees, not unpaid water fees, or anything else. So you want to be clear that money received first gets applied to those other things, and only the remainder gets applied to rent, that way if you need to evict you do so only on the basis of unpaid rent.
Also, tenants will ask you how much you estimate the water bill will be, and you'll need a reasonable answer for that. And realize that since most places don't charge for water, what you're telling them is that the "real" rent is effectively 50-100 higher than the advertised/sticker rent.
As far as bank account information, I don't blame the tenant for balking at your asking for account number or balance. I think that's an overreach and unnecessary. And in this age of identity theft and other rental-related scams, I wouldn't provide that information myself.
The bank isn't going to allow you to verify any information about the account anyway, regardless of whether you have the account number, so either way you're still taking the tenant's word that it's valid. If that's the case, just ask if they have a checking account and at which bank and stop there.
Also consider that you are cutting out a potentially large population of tenants with that requirement. I understand that you're aiming to screen for "financial responsibility" and "doesn't bounce checks", but there are many responsible people who don't have bank accounts (research "the unbanked"), sometimes for personal/family/cultural reasons. They simply prefer to deal in cash.
If you make it clear you only accept rent payment by check or money order, and once a check bounces they'll need to pay with money orders from that point forward, I think it makes it pretty clear that you expect to be paid a certain way and that you're above board with a paper trail, etc.
$40 for the background check (I'm assuming that's the only "application fee" involved) sounds a little high but it can be a valid way to try to weed out less economically able tenant applicants. You should definitely make it clear it's going directly to the screening company though. And remember, tenants - even good ones - are wary of scams so they may be reluctant to pay such a company if they've never heard of it. For all they know, it's a vacant house you broke into, and you're working for a scam company getting half of every application fee they rake in from "applicants".
I'm not saying not to charge an application fee, but try to think about it from the tenant's point of view and address those concerns if you can.
Lastly, you mentioned maybe moving in cruddy tenants for 6 months. I would advise against that. You would always rather have another month of vacancy than move in cruddy tenants who are more likely to be problematic, and then you have to fight to get them out.
I would try to be as up front with all of these things as possible, both in the ad and in the phone screen, before meeting them and taking applications. If you continue to find a dearth of qualified applicants I would strongly recommend taking the water off the table (even if it means bumping the rent a bit) and I would consider either removing the question about bank accounts entirely, or at the very least removing the account # and balance part.
Good luck and let us know how it goes, of course!