I think the “rules of thumb” (ie you have to leave space under recoil lug) are based entirely on rem 700 and similar recoil lugs. Yours is clearly different, so the same rules may not apply. In general if tightening the un-shimmed action caused the action to torque down into the stock and resulted in barrel contact, then thats precisely what bedding would solve.
(Disclaimer—I dont have a howa and have not worked on one). In your case bedding or a shim under the lug looks to me like the functional equivalent of a pillar on the action screw in a rem700/tikka/etc—you always support with full contact directly under the action screws with a non-compressable material so that neither action screw creates any torque on the action or barrel. The lug on yours is also angled on the front surface specifically so it wont bind as the action lifts out of the stock. If it were my gun, looking at how its configured and hearing how your shim helped, I’d 150% plan to have that thing bedded asap, WITHOUT any tape under or behind the lug.
That said I might not do too much if it has significant problems (bedding but also brake/threading as well as trigger). Even diy you could wind up with a expensive problem. I would not own a 16oz trigger on anything but a target-only gun, and a brake acting like that could be the brake or it could be bad muzzle threads. If its a keeper, great, fix it all…just worth considering.