Weight lifting movements should not attempt to replicate sports movements too much. Attempts to do so will necesseraly fail, even if one tries to recruit the same muscle groups and have the same, more-or-less, movement trajectory. The difference in movement speed alone, caused by the load, changes the timing, duration and intensity/amplitude of each impulsion and muscle contraction. If specificity cannot be total, then I am of the opinion that it is better to have less specificity so as to not negatively affect motor schemes. Add more overload instead.
So, for example, I wouldn’t go on a bench with a single heavy dumbell and try to perform a punch. If my mind thinks “I am punching”, I am affecting my motor pattern for that movement. I am refining it with improper parameters. Scapula movement, for example, is heavily restricted on a bench, but is crucial for a proper punch.
Instead, I may opt for a bench-press, but with a modified bench (think half-roll in the middle) to allow scapulae movement, or maybe explosive push-ups, wearing a weighted vest or with a few plates on my back. In either case, load will be sufficient, and I set my mind into “gym / physical preparation mode”, where my movements are different enough from my martial arts movements so that the addition of a heavy load will not interfere with the “x technique from y martial art” motor pattern. But, muscle stimulation will be there, hormonal changes will occur, suitable energy pathways will develop, neural drive too. My mental schema of the martial arts technique will be unaffected. (It will need to be slightly refined in the long-term to account for the physical changes caused by the gym exercises)
In other words, limit the domain of specificity in muscular physical preparation to:
muscle groups, contraction sequence (only the order of contraction), gross movement direction
Do not seek specificity in:
actual timing of contractions, precise movement trajectory, accessories used / training gear
From there, then, it is all a matter of the mind. What is the Intent, where is it focused, why and how.