I have 3 rentals now and the banks aren't very keen on giving me another mortgage with my self-employed income. 

First, look at lists of cities ranked by employment, employment growth, net in-migration, cost of living and other economic factors and find the top 3 on those lists and then start looking at properties and neighborhoods in those cities until you find one that grabs you.

There is some variability in the different neighborhoods.The best towns to do a house hack in my opinion are West Hartford, Newington, Glastonbury Rocky Hill, And generally any good Suburban town outside of the working markets.Primary employers are clustered along routes 91 and 84 and the Merritt Parkway.

So my first question is this: I'm using QB Self-Employed for our personal finances, would it be a good idea to simply invoice each business for my time that month?

Don't give up, you're in a great area that has seen high growth, almost zero vacancies, and is supported with diverse employment sectors and NJ and NYC transplants

I'm in real estate and/or I make my own schedule being self-employed.

Poor screening often results in lost rents, legal & court costs and costly damages.Screening of applicants includes the following:Full credit/eviction/criminal checks are done, instead of score-driven reportsVerification of rental history includes validation of actual property owner to avoid fraudVerification of stability of income & employment via YTD paystubs & W-2(s) (analyzed to confirm not fakes)Income is calculated 3 ways to spot stability anomalies: pay period, YTD average and YTD + W-2 average.Debt-to-income analysis (more accurate than traditional 3x rent requirement)Bank statement to see if NSF issues, if deposits support income, prove MoveIn Funds, also analyzed for unusual transactions.Pet screeningHolding Fee required from approved applicants to make sure they are serious, before a property is marked pending.

I've had many subpar experiences, quite a few bad ones, and more than one where I abandoned the place upon seeing walking into it.I believe much of the reason I've had lousy experiences is (a) I was trying to keep costs very low for my employer or client, so I often stayed in places that were in the $100-$175 range, and (b) I was often booking at the last second, which meant the best of options were unavailable, and meant that my options were either poorly appointed, poorly managed, or new and inexperienced. 

If your employer matches your contributions to any extent, you would be making a grave mistake. 

I read an article by Amanda Han (CPA, real estate investor, and very active member on BiggerPockets) where she gave an example of a lawyer who recommended the same structure of using one of their LLC's as the property management company for their client without realizing the huge tax implications of doing so (if I recall correctly, it had something to do with self-employment tax).