I like that you are considering a simple and standardized approach. However, there are a number of potential pitfalls to consider with this proposal. First of all, what specific RT activity are you trying to quantify? Is the the transcription speed or accuracy, or are you trying to characterize something else entirely? If you are measuring speed, how and what will you measure, reliably and will be reproducible, for speed? If you are going for accuracy, you will need a whole lot of sequencing to check the bases are correct. Both of these can quickly become expensive.
Also, is it necessary to use HIV-1 RT? Since you mention E. coli, would you want to consider using msr, a prokaryotic RT?
Though I've never heard or tried it myself, is it possible to transform mRNA into bacteria? I would imagine that it would be degraded as a natural defense mechanism. You may need to consider some alternative form of gene delivery, such as a standard expression plasmid. Genomic integration may not be necessary to achieve your goal.
As mentioned, you cannot just have naked cDNA to translate a protein. You need at least the promoter, RNA pol binding site and polyA signal. You could take advantage of viral infection systems (a replication defective HIV) to deliver your GFP and RT genes into a mammalian system (like HEK-293 cells), but this adds a lot of complexity and expense that may not be worthwhile.
The last thing off the top, you would benefit greatest from taking advantage of a directed evolution experiment to generate some potential leads. For example, you may PCR amplify the RT cDNA with an error-prone Taq to purpose create RT mutants for use in your assay.
Keep thinking about this, and maybe check the websites of the some of the RT commercial vendors. It is possible one of these companies have already done something similar.