I'm the same weight as you, 51yo, 178cm and fairly conditioned, advanced although feeling my injuries and possibly getting held back nowadays. YES, dropping volume, noticeably in rails, nose and tail, will reduce corkyness that you experience when you get backwash or sidewash and surface chop in less than ideal conditions.
I have a few too many boards

but like using them all when the vibe is right. I'll give a brief rundown of only a couple and what I've found from my experience of surfing in conditions from 1ft-10ft, and soft to quality hollow sucky waves.
JP Surf Pro 8' x 27" at 95L - surfs great in all sized waves, but comes into it's own in 5ft-10ft quality where paddle speed helps getting in compared to my 7'10" Acid. Holds in the face of steep waves if positioned right, and fits better in bigger waves so allows going more vertical in turns off the bottom towards the top of the lip. Gets hung up in this style of surfing in smaller waves for
Sunova Acid 7'10" x 26.5" at 80L - After lots of time on this board, it is my go to board from 3ft up to 8ft where is then lacks ideal paddle speed on the bigger waves but perfect at 6ft and below. I work a little harder on this board compared to the JP, but if has good stability and has noticeably less corkyness. A true high performance board that rips in sucky hollow waves and will handle and make anything that the user can throw at it with enough skill like knifing very late sucky take offs angled into the pit. By having reduced volume in nose and tail compared to the JP, the Acid at this size can be pointed towards a wave (me facing out to sea) and I can spin it much later to catch an incoming wave. Less likely to get bucked off by backwash, sidewash and chop due to lower volume sitting more in the water. Lower nose volume allows punching through chop and lips of waves when paddling out than the JP.
Sunova Acid 7'4" x 25" at 70L - Hard work for me and I can only ride it in groomed conditions to 3ft so far. It RIP's but I'm not pro enough to get the payback (yet

). I rarely ride it but will not right it off.
Sunova Insane 8'11" x 26.5" at 102L - The 8'5" would have been better but I found it cheap so why not. It excels in juice, 6-10+ft, as it's super sure footed when dropping down into meaty bombs. Does what it's meant to: turns great with predictability, good paddle speed to get in early when most are struggling in the big days, holds in the face with confidence. The volume is only a hinderance for me when it's bumpy and messy as it bucks me around a little.
Final note: All these boards allow for getting out in bigger conditions as they are still on the lowish side of volume and I don't get dragged back to the beach too much to not make it impossible. A high amount of fitness, skill, and timing is still required though.
Take the leap, and don't be afraid to make bigger increments in volume drop. The brain will train itself to cope after one hour if you are pretty physically conditioned, and the waves you'll surf well will put a smile on your dial forever