Hello Ryan,
I'm pleased to read that your Dad is recovering well.  Primary liver cancer is
hard to stop.
http://www.rxlist.com/cgi/generic/zadaxin_ids.htm for ZADAXIN thymosin alpha 1
(thymalfasin) shows that it's for hepatitis? along with interferon.

Later, when he's fully recovered, you and he may wish to ask about clinical
trials (or ask later, if more cancer starts showing up).
I found one;it's in combo with chemoembolization and one of the criteria is
inoperable.
Biopsy/pathology is required.
http://clinicaltrials.gov/ct/show/NCT00082082?order=1
It's Phase II trial which measures for efficacy and toxicity.  As best I can
tell from another patient, chemoembolization can be as hard on the body as
surgery.  What is your Dad's age, please?

I suppose you could search yourself with the word HCC and then with the word
liver: Carcinoma, Hepatocellular
This is what I use to search.
http://clinicaltrials.gov/ or use "Studies by Condition"
The goal and objectives are usually mentioned for each trial.
Actually, I selected alphabetical "liver neoplasms".  There's 55 listed there.
Of course, it may be easier to just ask his oncologist, at that time.

In the meantime, I wish you both well. Keep in touch and let us know how's it
going.
J