How are you planning on performing your transduction? Are you going to dissociate the tumour before transduction or are you performing transduction before you make the tumour? What type of tumour is it? I think you can use puromycin selection- or you could select GFP positive cells using flow cytometry. I used a GFP lentivirus for transduction of mammary cells to make subQ tumours with about 70% transduction efficiency. I added the virus, incubated for 4 hours at 37 degrees then washed the cells. After 24-48 hours I selected the positive cells using flow and then injected them. I didn't use polybrene in this case as I had high efficiency, however, when I did transduction of mouse keratinocytes my efficiency was much lower so I used polybrene, which helped matters.

Keep reaction volumes low. This will increase transduction efficiency due to vastly improved virus to cell contact. In cases where tranduction was a I have used volumes as low as 100 ul containing 100K cells, due to the low volume however, restrict incubation times to no more than 20-30 mins.

We routinely use lentivirus for introduction of GFP and RFP in various tumor cells. In my experience, depending on the titer of course, most cells are happy with an over night incubation before exchanging the medium. In addition, polybrene will increase the efficiency but, as the first comment above mentioned, it could be target cell dependent if necessary or not. Selection with puromycin could, in my case, help to enrich the positive population to ~80-90%. Sorting by flow cytometry allow you to expand the brightest cells. Good luck!