Should I even consider leaving at this stage?
I would, if I were you, based on the push factors (at your current work) and the pull factors of this potential new job.
You haven't been offered the job yet, and have made no promise about jumping ship. so you've really got nothing to lose by applying/interviewing for it.
I'm very harsh about job hopping when i interview people at work (generally I'm involved in 2nd-level meetings, not the filter-style first interviews).
I really don't want to let my managers down, and I know they would be very disappointed.
You need to put yourself first. Fine to consider your current employer, but you aren't "letting anyone down" or disappointing them - if they are, and you've given the correct notice/dealt with the departure professionally and they still get irked, they're not very professional.
Employment is a business transaction. It isn't always just that, but it is primarily. You give your skills in exchange for payment. Don't forget that. Don't also forget that if the business was struggling, the owners/CEO wouldn't feel terrible (personally) they're having to let you go, if it was business-driven. They might feel bad about letting someone go, but it would have been a business decision. Not an emotive one. You should think of your employers in the same way, IMHO.
In addition, I have had enough trouble in the past explaining to prospective employers that the reason I have so many temporary roles on my Cv is due to the fact they were temporary and I needed to work - there was nothing more permaanent available.
This is a perfectly valid excuse, as long as it fits with the profile of the jobs you've been working in e.g. I know a few people have tried to pass this off at interviews in the past for companies where I know they mostly favour permanent staff, not freelancers - so I've queried the contract status at reference checking just to be sure they're telling the truth. If it is the truth, there shouldn't be much concern, because they should know the job market that you've been working in.
how would I convince any future employer that I am not just a flake and I really do want permanent, long-term employment
You should just be clear about the things that any employer is going to understand, as the other posters have said. Shorter commute, etc. You might even list "a better benefits package" if they probe for more reasnos - just make sure that you don't come across as someone who would jump ship at the drop of a hat if someone else offered you a payrise. But that's the point where you'd give examples of why they are a good fit for you, and vice versa (and re-inforce stuff like wanting to get involved with some of their outstanding client list, the location of the office being more practical, always wanted to work in this area of the industry due to XYZ....)...
that's just my opinion, i'm not in HR, i'm merely a "second opinion" at most of the 2nd level interviews my employer does.