I am not sure on a good DT. In the past I have used Suave but I know some have protein so you'd have to check ingredients. To get it done with what you have on hand you could rinse hair very well with very warm water for several minutes to open the cuticles, apply conditioner, place a shower cap over your hair and let warm water run over the cap for several minutes, then rinse in warm water and apply LI while still in shower. This is how I do my conditioner every day now but it is sort of a mini DT. Might help at least a little under the circumstances until you find a thicker DT conditioner.

You can also do all steps up to running water over the shower cap - instead of running water, apply a hot towel over the cap and cover with another cap or plastic bag. This helps seal in the warmth. Keep this on for half an hour or so then rinse with warm water.

Please be careful to not over-condition now as you figure out your protein-moisture balance. *sigh*
remember, with all advice or suggestions for your hair, YMMV!!
My hair:
2b wavy, medium texture, low porosity, med-high density. Protein finicky.
My routine:
Cleansing: DCNP, every 4-5 days (occasionally use CJ cleansers).
RO: CJSC, occasionally use JCDC
LI: KCKT or CJSL
Gel: KCCC, CJCIAB for 2nd day hair (sometimes third)

Heat is my friend: warm water rinses, steam caps, and diffuse dry. I love CLU cloths and my Denman.