Most chips that have a hold-down of some kind heatsink, I just use a paste/compound. The Noctua paste is "cheap" and effective. I use it on pretty much everything. VRM and memory still get pads, though. Usually because something NEEDS to fill the space.
I'm noticing now, that heatsink looks like it was soldiered on, but does have an "easy target", mounting it flat with paste should be do-able.
If you're paddin', pretty much ANYTHING is better than the stock one. I would indeed go with the thinnest one.
Daily Units:
ASUS P55TVP4, P-MMX233, Matrox2064W, CT2770
ABIT IS7, P43.2(SL7E6), PNY6600GTS, Audigy(0090)
ASUS M2N-SLI, A64X2-5600+, EVGA 8600GTx2, Audigy2(0240)
ASUS ST-990FX, FX-8350, MSI GTX760x2, SB X-Fi(0460)
MSI Z690, i9-12900K, MSI RTX3090, SB AE-7