1st dilemma: As I suppose you’ve guessed, there’s no way to incorporate the exact phrase avoir beau into both predicates the way they’re currently worded, because the expression is tied to the subject and you have two different subjects. (Of course, you could repeat it if you wanted: « Il a beau être un vieux bougon et on a beau se quereller … » )

I think you have the right idea with a sentential adverb like certes since that can easily be made to qualify two different verb phrases with good punctuation:

Certes, c’est un vieux bougon et on se querelle souvent, mais…

However, I wouldn’t say that avoir beau is that close to certes. I’d translate « on a beau se quereller » by something like “For all the good our quarrelling does,” whereas « Certes, on se querelle » would be more “Admittedly/It’s true, we quarrel.” But that might be the meaning you intend anyway. In any case, I think this syntax is a pretty likely candidate for applying such a modifier to both elements.

2nd dilemma: Agreed: c’est and ce sont seem too invariable to support anything interposed along the lines of « Cela/celui a beau être … » , at least not with the same meaning.

Also, if you do stick with avoir beau for his being an old grump, I wonder if a more active verb than etre would better complete avoir beau (which to my mind carries some sense of intentionality)?

If you want to include the expression avoir beau for the two clauses, they need to have the same subject (or you can repeat the expression, but that’s a bit inelegant).

You can get there by slightly transforming the second clause:

Il a beau être bougon et se quereller avec moi souvent…

I’d also consider merging the two clauses:

Ce bougon et moi avons beau nous quereller souvent…

J’ai beau me quereller souvent avec ce bougon…

On your second question, you have to drop the article un in front of bougon to make it an adjective. With un the meaning changes:

Il est bougon = c’est un bougon = he’s grumpy, he’s a grumpy guy

Il est un bougon = (old) there is a grumpy guy