Repetitively emailing old lab group about a paper constantly on the backburner Context

About a year ago, I left a research team that I was involved with as a student for approximately 2 years. During this time, I did a variety of unpaid internships and paid scholarships as well as doing a year long research project for my degree with them. Throughout the 2 years, I was working with them towards writing and submitting a paper about the work I was doing. 

After I had finished my degree, I asked to stay on as a member of staff. Whilst they were interested, they unfortunately could not offer me a job so I had to look elsewhere as I couldn't simply work for free forever. I soon after received a job at another institute and made plans to leave. Before I left, the paper we were looking to submit was in its final stages of completion. I had written a fully referenced draft, completed all of the figures and done all of the stats on the data. We were planning to submit within weeks of me leaving.

Note: I had left on excellent terms with them and they were very happy for me that I had managed to find work.

Issue

However, it's now been close to a year and things still have not moved. I've emailed them 4 times in past year (at least 3 months inbetween each email), telling them how things are going in my new lab and to ask if we can have an update about the paper and also asked if there's anything I can do for it such as re-analysing data or re-working any figures. They reply with either "currently a bit bogged down with grants/other papers/etc" or "we're aware of it and we'll get something to you soon".

I've tried not to pester them about it and I'm concerned about crossing a line by contacting them incessantly. I'd like to remain on good terms with them.

How should I approach this situation? Should I let it go and be pleasantly surprised if they contact me? Do I risk annoyance by contacting them further about it? I'm aware that yes I did leave and no it may not be in their highest priority, but it's still a publication for their lab. There is a mutual benefit for us.

I have also considered the fact that perhaps it is not as complete as I had thought and that they need more data. But insofar they haven't communicated anything of the sort to me.

I'd really like to have my work published. Not just for ego reasons, but I will be most likely applying for some pretty competitive PhD scholarships this year so would also like to have at least a first author publication under my belt.
It's naturally to everyone's benefit to get the paper published. However, it may also be the case that your former PI and co-workers may not have the time and focus to work on it themselves.

Perhaps the best way to get things moving again is to change your question. Instead of asking a variant of


  Will the paper be submitted soon?


try asking them what will help them:


  I know you're very busy. What can I do to help get the paper submitted?