If pay at the top of their grade for lecturer is lower than you would accept, it really would not be simple for them to pay you more. There is a nationally agreed pay structure and this is another case where they'd have to consider everyone else in the university. A lecturer role is paid at a set rate. If you're appointed as a lecturer, they can't exceed that.
What you could look at is requesting a 75% part time role and being paid directly, 25% of salary from the research institute. That might not be attractive to the new place, but you never know. Even under your current arrangements it's not obvious who gets credit where REF is concerned and I'd presume that and student fees stay with the institution. If I were involved I'd be trying to sort out a formal partnership with the institution - maybe they can do that but not in a job offer timeframe?
You are making a mistake here thinking about your profile and experience instead of the role. But it's the role the university wants to fill. In an 80% teaching role they're presumably going to want a fair bit of teaching and course admin and a strong contribution to the dept. Managing 25% buyout is a pain - somebody is going to have to recruit, train etc for these roles.
My heart would be sinking a bit if I were your prospective manager. Do you want the actual job they advertised or not? Do they get concrete benefits (not reputation / networking) from the secondment? Timetabling and managing two people is more complex than one, and the 25% is always a recruitment struggle / flight risk. If I was very keen to have you and you seemed keen on the rest of the job I'd be trying to make this work, but I wouldn't anticipate that it would be easy.
Another route to consider, if your research has commercial value, is whether the university has a commercial services dept that could agree profit arrangements.
But while I can see this is an attractive proposition to you - higher salary, keep current links and projects - I don't think it's a fit for the role. Be receptive and open minded in your discussions.
We would come under pressure to agree or ask you to reject the offer within a week or so, unless no other candidates had been appointable.
Your best bet is top of scale, all available info about progress to SL, think about concrete benefits of 25 per cent buyout to them, think about what aspects of the role you can and can't do at 75 per cent. (A course leader role might not be possible but might be expected at SL).
You seem to have very little teaching experience. Should you be top of scale at L? It's an 80% teaching role.
Hope this is helpful to show some possible complications - they may like you and want you but what you are requesting isn't simple and may not be possible, so don't take it personally if it can't be done.
Good luck and well done on the offer.