No. There's no way to get HSS from a Yongnuo YN-560 IV.

HSS requires camera/flash communication along the flash foot pins that the YN-560IV doesn't have (being single-pin. That pin is for the sync/fire signal). And the built-in radio transceiver of the YN-560IV & YN-560-TX combo doesn't accommodate HSS signalling over radio, like the Godox TT600 & X1T or Cactus RF60 & V6II (also single-pin manual-only flashes) can.

With Yongnuo gear, the only triggering systems that accommodate HSS are the 622 triggers/lights (e.g., YN-685 & YN-622-TX), and the -RT triggers/lights (e.g., YN-600EX-RT II & YN-E3-RT).

Theoretically, if you hooked the YN-560IVs up via PC to YN-622C triggers, you might be able to do tail-syncing (aka hypersync, supersync, etc.), but I was never successful getting my YN-560 (I) to do that, only my 580EXII (which of course is kind of a pointless exercise, since the 580EXII does HSS).

The ND filter trick may be your only way to get thin DoF in bright ambient with fill flash, but remember, you're still not actually getting a faster shutter speed. So if your HSS requirement was for freezing fast action in bright ambient, that's still not going to work.

You can, however, buy a single ND filter in the largest size you need, and then use step-up rings to fit it to smaller lenses. The problem is knowing how much ND darkening you'll need in a given situation. Variable ND filters is one way, getting a set of NDs of different concentrations and then stacking them is another.