If you don't spend additional cost, it is cost free, if you have no downside risk, it is risk free. In a nutshell you are looking for a risk free cost free way to profit from your CC?
Trying to neutralize the position risk at lower cost than outright put.... was thinking if act before price gets to strike, I could sacrifice potential CC premium to get lower cost “insurance”.
The problem is that you have already decided that you want to buy that put, so no matter how much sensible advice you receive, you won't change your mind. The only way you could pull this off is by legging into a trade where you were initially correct on direction, so you already got some profit, the puts likely dropped in value and you can afford to buy them while preserving a part of your gains. At that point however, it would still make more sense to close the trade rather than to buy a put.
Doing that with covered call does not make sense as your gain is limited. Own a call outright and you run up a huge gain makes more sense.