A good chromatic tuner should be sensitive over the entire range. Tuning 50 cents flat is not an issue other than the target pitch is not dead center. A tuner showing cents sharp/flat is preferred regardless of tuning choice (over colored LED styles).
The capo idea is good as well, but I would suggest finger-fretting each string rather than a capo itself. As mentioned above, they can pull all strings sharp depending on placement, capo spring tension, and fret height.