Is there an unorthodox way to memorize formulas for daily use, similar to the assimilation of multiplication tables in primary school? I included ‘without understanding’ because I do understand the formulas: given pen and paper and time to think (about the physics involved and/or dimensions) I can figure out the formula. I need to be able to use them instantly, without thinking.

Some context:
I am a physicist (PhD student) who has spent about 7 years in the field. I thought that I would by now automatically have assimilated formulas that I use daily, but this hasn’t happened. If anything, the situation progressively worsens because I vaguely remember so many formulas that I mix up similar ones. I can never come up with a formula when asked on the spot, which is embarrassing. On my desk I have stacks of formula sheets that I have to use continuously, including highschool-level formulas, which is very time-consuming.
Examples: trigonometric identities, \$lambda = c / f\$, \$k= Omega^2 m\$, hamiltonians, derivatives etc.

A long time ago when I studied Latin I managed to learn meaningless sequences by heart by repeating them hundreds of times (orally an in writing), rhyming, making songs etc.
This is also the only approach I have found thus far for physics formulas, but the problem is that I need them every time in another form (\$k= Omega^2 m\$, \$ Omega = sqrt{ k/m} \$ , \$ Omega^2 = k/m\$, \$m = k / Omega\$ and so on). This means that I would have to separately learn by heart all different permutations of a formula, which is too much.