I don't know portrait work from nothin', so take the following FWIW...
We did use a foam board for a reflector in a few of the shots but not this one.
Built this the other day, based on member
@ac12's suggestion, I believe it was:
It's aluminium foil tacked to cardboard with spray-on adhesive, non-shiny-side-out. (N.B.: He suggested crumpling it, with shiny-side-out, I assume.)
I haven't tried it, yet.
I really like working with continuous light.
I prefer it, too, but what I've seen and read suggests sufficient continuous light is
really expensive.
I had to bump the exposure on almost every shot. I wish I had moved it a bit closer.
I have read that the further back you can be (w/in reason) the less it freaks out your subject. There are also DoF considerations, from my limited experience with other subjects. (Mainly cats

.)
Do continuous light and flash mix?
Heed colour temperature.
I have an OttLite I bought for macro work. It's
alleged to have a colour temperature similar to daylight. I
believe speedlights are a similar temperature. But normal room incans, LEDs, fluorescents, halogens, etc. would be a mismatch. A white card can't fix that, because the different light sources will almost certainly have different angles of incidences.
I
have seen professionals that came in to do product photography where I used to work use continuous light and speedlights together. They'd have these gigantuous reflective umbrella things set up to light the entire "stage," then speedlights in addition.
Re: The photo. My only thought was the shadows were too deep, but, as I said: I don't know from portrait photography.