checkout PS2HD.com it's an awesome growing community and they've started an awesome compatiblity list. The list shows both HDL/HDA and ToxicOS compatiblity, and links directly to hosted patches.
To answer your issue Gradius 4 JPN is compatible, but Gradius 4 NTSC USA is incompatible. As for Half-Life you must install it using HDL_Dump/WinHIIP to bypass load problems.
I found this info at PS2HD.com in their compatiblity list. List Here
Smoke V5 SCPH-30001 R
DMS4 EZI Pro w/ ToxicOS 0.3
250GB Hitachi DS 7K250 HDD