Very partial answer, not much more progress than anyone else yet but never mind. First of all, some answers to clues (some of which I'm happier with than others). Some of these were first found by other solvers and you can see them in comments and other answers. Some of them (even ones found elsewhere) I found independently, but feel free to assign credit for all of them to other people :-).
SECANT 1 2 10 15
KEENLY 4 7
CLINGY 4 7
UNSEAT 1 2 10 15
TOOLED 8 13
PRIEST 1 15
ENDASH 3 5 11 12 14 17 18 19
GRATED 3 5 12 14 17
HONOUR 6 9
FOURTH 6 9
REDOWA 3 5 12 14 17
SEDATE 1 2 3 5 10 12 14 15 17
???
BREADS 3 5 12 14 17
DETACH 3 5 12 14 17
LOOTED 8 13
???
???
ARDENT 3 5 11 12 14 17 18 19
The things I'm least satisfied with there, apart from the outright unsolved ones, are
GRATED (seems like the clue should be referring to the food rather than its property), HONOUR (assumes British rather than American English; I don't know which Alenanno prefers), BREADS (the S is from "sunrise" and seems rather unsatisfactory), DETACH (surely there should be something better).
In Sphinx's Lair chat there has been a little discussion of one of the clues for which I haven't proposed a solution and
ERUPTS has been mentioned as possible for "lose one's temper", but it seems wrong in something like the same way as GRATED.
So that leads to the following residuals for our dice:
! 1 CAN AUN PRI EAD ! 2 ECN EUN EED ! 3 NSH GRT ROW SET BRS TCH RNT ! 4 KEE CIG ! 5 NSH GRT ROW SET BRS TCH RNT ! 6 HON FTH ! 7 KEE CIG ! 8 OOD OOD ! 9 HON FTH ! 10 ECN EUN EED ! 11 ESH RET ! 12 NSH GRT ROW SET BRS TCH RNT ! 13 TLD TLD ! 14 NSH GRT ROW SET BRS TCH RNT ! 15 CAN AUN PRI EAD ! 16 ! 17 NSH GRT ROW SET BRS TCH RNT ! 18 ESH RET ! 19 ESH RET
which rather suggests that
for dice 3-10 we might want .../CHT/HON/IC G/OD O/F TH/E DE/... although if so we had better find something else for die 11 because neither EST nor ERT seems to go well after that; we surely want that last word to be DEAD or DEEP or something. (Aha, no, we can do better; see below.)
Another place worth a look is
die 13 which (unless one of the unsolved clues provides something helpful) seems to have to have a residual of TLD, and be both preceded and succeeded by quite consonant-heavy stuff. The best I can find at present is .../WOR/LD T/... but if so then I think we need something else for die 14. And, aha!, we can join these two blocks together to get CHTHONIC GOD OF THE UNDERWORLD which sounds awfully promising. That would mean that die 11 has a residual of DER so that word is an anagram of ADDENR; perhaps DANDER is the intended answer to the clue about losing one's temper, though I don't think it actually quite works if so.