There are lots of different ways to breed, rear and keep this species. You will get different answers from different breeders (but stay away from "the best breeder in the world" - for now anyway). There are a few basic characteristics that you should always consider;
1. male instinctively care and rear eggs and fry. Good fathers will keep eggs clean from mold and later feed newly hatched fry. UNFORTUNATELY many have changed. Now you will find many different behaviors; males not picking up nor tending the eggs, male eating eggs and fry, etc. I'm not saying that there are no good fathers anymore. I'm just saying that you have to treat every individual male differently.
2. Glass is a better heat conductor compared to plastic and thus heat will fluctuate more in glass tanks. BUT new to breeding should IMO breed in something they can easily see through so they can understand bettas behavior, determine when spawning is done, spot problems as soon as possible, etc.
I suggest you use the 10g glass tank method. Ideal and easier to care for fry. Later move them to a bigger grow out (after a month or so).
Since your male is a fry eater but cares for eggs, you can leave male in until fry are free swimming then immediately remove him. When you're dealing with known egg eaters, you will have to remove male as soon as spawning is done. You can leave eggs and hope for the best or you could move eggs to a small clean bowl and artificially hatch them.
I suggest you cross DTHM / DTHMEE x VT. Though you might get odd looking fry, yet they will be easier to work with compared if crossed to the CT. If possible, breed daughter back to father. Hopefully you will retain the HM trait.
Btw, welcome to the forum.
Good luck and keep us posted.