Expanding foam with a proper gun is quite controllable. Worth investing in a decent gun.

I would PU foam fill, cut off the excess (I found a bread knife quite useful!) then aluminium foil tape.

As a DIYer, I spent a long time trying to cut boards accurately to fit tightly, shaving a bit off here and there.

Now I have given up and cut them deliberately 3mm too small all round, they fit first time and I can get a good squirt of foam into the gaps.

Posted By: WillInAberdeenAs a DIYer, I spent a long time trying to cut boards accurately to fit tightly, shaving a bit off here and there.

Now I have given up and cut them deliberately 3mm too small all round, they fit first time and I can get a good squirt of foam into the gaps.

100% agree - I too found out the hard way! Buy a professional foam gun with low expansion foam. The flow is easily controllable and even if you overdo it a bit, there is not much waste with the low expansion variety. When it's hardened, cut off the excess with a sharp, non-serrated, bread knife.

Posted By: Jeff BPeter - the OP intends to use PIR boards though?

Oops - However
another study
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiQvOGT293-AhVPhf0HHSExDq8QFnoECD0QAQ&url=https%3A%2F%2Fwww.mdpi.com%2F2073-4360%2F14%2F22%2F4926%2Fpdf&usg=AOvVaw1aC9x6tHTykQ9Fetn0NkNN

Abstract: Foam insulation materials are widely used in the construction industry due to their low
thermal conductivity attributable to their microstructures and their low-conductivity blowing agents
and affordability. In this study, we evaluate how the thermal performance of foam insulation materials
used for the exterior walls of buildings, viz., extruded polystyrene (XPS), polyisocyanurate (PIR),
and phenolic foam (PF), age over the life cycle of a building. To compare the aging of thermal
performance during the life cycle of a building, each material was tested at 70 and 110 â—¦C and with
slicing acceleration according to EN and ISO standards. The thermal conductivity of each foam
insulation material was measured using a heat flow meter at an operating temperature of 23 â—¦C and
converted into thermal resistance values. Different foam insulation materials have different aging
procedures according to material-specific EN standards, while ISO 11561 applies the same procedure
to all material classifications. Upon comparing the aged values according to ISO and EN standards
to the initial values, the analysis showed a change rate of 23 to 26% in PIR and 18 to 20% in PF. In
XPS, a rate of change of 10 to 23.8% was calculated

End Quote

So it would appear that solid board insulation will degrade over time with heat. I suppose the next question is - will the temps of the insulation under tiles get to the temps used in the test? Probably at the top surface but not all through and what degradation over time will be seen (if any) in real life application.

Glass or mineral wool is good to about 1000 degC is cheaper than board insulation but greater thickness is needed for the same U value and whilst easer to instal (IOM) they can suffer from slump over time and compression of the wool can result from careless installation.

Any advantage in using PIR on the north and east side and glass/mineral wool on the south and west side ?

I wonder what the insulation value of 'squirty foam' is and will using it to fill the gap in the insulation create a cold bridge?

A builder told me about a job he was on. He had previously done a build for a client who called him back some 10 years later to do an extension. This involved stripping back the roof he had previously done. To his horror he discovered that there were big gaps between the rafters and the PIR. They had shrunk with edges forming a concave. When we did our build we put 170 mm rockwool between truss rafters and overlaid 100mm PIR boards and taping joints and fixings with aluminium tape so as to avoid such an event.
When it came for us to do the floors I ordered 100mm and 50 mm boards to cross lay but when they arrived the 100 mm boards were concave all around the edges they had shrunk in the same way as the builder had described. They were rejected and replacements obtained. The merchant accused me of being too fussy and any one else would have used them. One of the reasons I reckon why houses do not perform.
Coming back to the original posting I recall some years ago seeing at an exhibition a foam tape product you wrapped around the slightly undercut board and push fitted it between rafters and the tape took up the gaps. But if the board shrinks then not much use I guess. Recall it being expensive I not recall the name of it.

Posted By: djhDoes the aluminium tape stop the boards shrinking then?

I can see the ambiguity in my post. It is the rockwool that prevents the shrinkage not the taping.
I would not have thought tape would be enough to stop shrinkage it would probably pull off or split but In my situation as there is the 170 mm rockwool between the slate roof and membrane so guess would not get hot enough. The joints between the boards rest on the truss timbers this also avoids the "cold bridge" through the timber the tape helps make the joints more air tight. The boards are secured with long screws and plastic wall tie retaining clips for insulation into the truss timbers. The screw heads and securing rings are also taped over. Having had the report from the builder and my experience with my delivery I wonder if PIR between rafters is a good idea. I also wonder how SIPS roofs behave.

Posted By: revorComing back to the original posting I recall some years ago seeing at an exhibition a foam tape product you wrapped around the slightly undercut board and push fitted it between rafters and the tape took up the gaps. But if the board shrinks then not much use I guess. Recall it being expensive I not recall the name of it.

For anyone else looking, I think the product you're referring to is Gapotape.

Oww! 25mm gap! That's a hell of a lot. And phenolic is reputed to be bad!