Adding grip tape to the slick painted metal of my dip bar has enabled me to progress further into the front lever. It's a big improvement. I did a bunch of research into grip tape before hand, and existing information is pretty vague, so here's my information.
Howie's (Non-Stretch) Pro Grip Tape is a very tacky and moderately coarse cohesive grip tape, meaning it has no adhesive, it sticks to itself. It sticks very well to itself, almost too well because it's a pain to get the tape off the roll. Popular among firearm enthusiasts for being a cheaper alternative to firearm-specific rebrands like Goon Tape. Despite this, it's actually pretty expensive for a small 5 yard roll of the stuff, enough for one dip bar plus maybe some leftover.
Upon further research I learned that cohesive tape is primarily sold as vet wrap, as it does not stick to fur. It's sold in the stretchy style (Howie also sells a stretchy variant of their grip tape) and is much cheaper than Howie when purchased from Generic Chinese Supplier #420. I tried this, getting 12 rolls for less than the cost of 2 of the namebrand. It would definitely work as a cheaper alternative but the non-stretch stuff is just way more tacky and grippy in comparison to the vet wrap. Since the vet wrap is stretchy it also can shift unless you apply it specifically to avoid that: fully-stretched the vet wrap as you apply it, and be generous with the overlap. It's still an improvement over the slick wood of my p-bars so I'm leaving it on..