Look up Blackjack hardhat clips. They’re a narrow u-channel with 3M tape for mounting. They work great, lots of oil hands around here use them. They seem to stay put unless you have heavy exposure to oil vapor/solvents/extended time in contact with water, but if they work loose you can retape them or epoxy them. The clips mentioned above are easy to slip out of place and break…Milwaukee does have some that are a little better but I think you’d have to contact Milwaukee or your local service center to get some (only included with their lights). Petzl also has some that might work…rubber coated flexible clips that you wrap under the rim. Also, not sure if anyone else is doing this, but Klein has a whole lineup now of headlamps that are made to clip onto hardhats made for them…not terribly expensive but the lights may not be what you like.
If you use the zip tie mounts, the adhesive on those is often sub par from either poor quality tape or poor storage conditions, so clean the hat well and press those on hard for like a full minute each and leave them alone for a couple days if possible (or buy new UHB tape…or VHB if that’s all you can find).