My hair is very dry also.

I think the tresseme naturals has aloe in it. That behaves as a protein for some people. Unless you know aloe is ok for you, you might consider taking that out of your reglar routine (aloe is the only 'protein' I can use but I still have to be careful with amount and frequency.)

Your siggy says your hair is low porosity. You might be able to do a DT with the suave or your RO. But, use heat! Saturate your hair with very warm water for several minutes, apply conditioner and work through your hair. At this point, you have two options. If you want to do this in the shower, apply a shower cap and run the warm water over it for several minutes then leave the shower cap on while you finish up your shower. Remove and rinse the conditioner out. You can also do this out of the shower: place a bag or shower cap on your hair, place a wet warm towel over that, then a shower cap over all. Leave on for a while and rinse with really warm water.

I still plan to add a true DT once a week or so (but I have to use online boutique stuff so I can't help with drugstore recommendations) but my hair has improved so much just from doing this "steam" treatment with my regular RO.
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
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.