I'm not massively bothered about how great the lambs turn out
Just as well.
It seems bizarre to be talking about castrating a purebred ram to use a Bitzer
If you like Bitzer so much why not castrate him, keep him as a ram companion, and use the welsh ram?
On your scale, linebreeding one generation
and not keeping the offspring for further breeding is probably not a problem.
Having said all of which, we buy purebred, often pedigree and very occasionally a controlled mix of two breeds (eg 1/8th Beltex, 7/8th Texel) tups. I've fancied using a Beltex x Charollais but BH says it's best to keep the tups purebred. However, every year get a handful of unintended early lambs where an uncastrated tup lamb had managed to get busy before we got him away. Our ewes are mixes of several breeds, so the tup lambs will be 50% Texel or Charollais and 50% allsorts. Their unplanned offspring are always absolutely fine and sell just the same as their 'better bred' peers.