I have 4 airheads that I am responsible for. 2*R100RS, the wife's R65 with R80 engine. All of these have stock(ish) suspension and Ikon shocks.
My R860 has a K100RS front end and custom made Betors. The wife's bike wears Pirelli City Demons, the 860 has Highway demons. One RS has Avon's and the other has Contis.
Now it tested each of them after fitting the tyres and strangely enough I arrived at the same solo tyre pressures for each of them.
Namely 34psi front and 36psi rear, these pressures go up a few psi if carrying a pillion or luggage.
The tyre pressures stated by BMW back in the day should be ignored with prejudice.
As regards stability the 860 tracks like it is on rails and I have herded it over some fairly indifferent surfaces.
The R65/80 is likewise stable, but perhaps notctocthe same extent as the 860.
The 81 RS has shown occasional signs of nervousness and has given the bars a bit of an incipient shake a couple of times but hasn't ever looked like developing into anything.
Back in 1983 or thereabouts the 78 RS scared the crap out of me several times. It would suddenly enter a violent tank slapper at about 70kph that would continue down to 50kph and self terminate.
Make no mistake, these were violent, full on tank slappers, on one occasion the violence was sufficient to break the retaining locks and spit both panniers off.
I used to transit through the onset speed, both up and down, as quickly as I could, but to be honest the bike scared me spotless.
After consulting widely I took off the Pirelli Phantoms and went back to motel traditional tyres - Metzlers if memory serves.
The change in tyres tamed but did not completely remove the tendency to shake its head.
Not until some years later did I discover that the centre hole in the triple clamp top plate was worn oval. I replaced the top plate with a Luftmeisterachined alloy top triple clamp and it has never shaken again.
My own postmortem thinking is that the Phantoms were for whatever reason unsuitable tyres for an airhead and the tank slappers damaged the top plate and replacing that completely cured it.