Great advice so far. The key is to document and to communicate both up and down the organization so everyone is fully briefed prior to departure. An organized file cabinet and a briefing book should cover most situations.

I disagree about leaving any option for a subsequent consulting gig. Leave your contact info, of course, for incidental questions requiring only a brief phone conversation. Otherwise make it an amicable but clean break. Your next job deserves and requires your full attention.

Your new employers are your employers now.

The fact these guys stuck their heads up their asses is no longer your problem.

Make sure that you completely load up the back of your car with all the office supplies from the supply closet before you do that

In fact, I'm looking right at it.

It's a Swingline stapler, but black, not red.

When you're outta there, you're outta there.

I left companies when I was in the middle of projects (due to the nature of the business, I was always in the middle of projects). They figure it out. Life goes on.

is not addressing the problem because doing so would require painful choices. My recommendations, in part summarizing below:

1. Do your job to the best of your ability for the rest of your time with the company. That alone can be a challenge as "short timer syndrome" is not a fig leaf (intentional) of someones imagination.
2. Document what you can. This starts with the project management tasks. Make sure your MS Project schedule (tool assumption based on size) is up to date; highlight any tall poles or problems that should be watched for over the next month or so. Red font, yellow highlight as needed.
3. Inform your current boss(es) on any critical items. That starts with subordinates who may be especially capable (possible replacements) or require extra attention. Quality concerns would be number two on my list.
4. Brief your current team on what is going on.
5. Leave your contact information and consulting rate as suggested. Be generous with your current employer with willingness to answer straightforward questions as needed over the next month or two; be generous with yourself if they start to abuse the privilege (doubly true for the SME aspect of the work).
6. Keep your new employer (assumption on my part) informed about what is going on with the firm you are leaving and make sure that old loyalties do not interfere with new responsibilities.

Fair winds and following seas!

Establish a cutoff point where they're on their own - doesn't have to be stated, just in your mind at some point you'd say "OK, enough is enough". Usually, though, it's a moot point. They figure it out and move on and don't bother you.

On point 6, that only works if you tell the new employer before taking the job, and the cutoff point again is critical. You can't tell them after starting the new one. I'd ask "who do you work for, them or us"? We had a recent situation like that, with an absolute top-notch consultant but she was unreliable because we didn't know if she was working for us or still working for her old clients. She was independent for many years and it pretty much seemed she wasn't getting the "you work for us now" thing, and there was a parting of the ways.

The people paying you have to know they can count on you. And that means all the time.

before consulting for them indepdently.

Unless your contract obligates you to identify your replacement or is an express contingency on your getting some kind of severance, I see no obligation. Speaking as someone who is not your lawyer.

If they are the kind of organization that will trash your name in the industry and you care about that, then that could be a consideration.

with your contact info and your hourly consulting rate.

To provide someone ti whom you can transition. If they do not, you’ve left materials for the next person when they do.

However, consider letting them know what your plan is and suggesting they identify someone - even if interim on their end.

Do what you can to tie up loose ends. Generate documentation where possible.

Otherwise, don't worry about it.