I've had shin splints in the past, last year infact and they are horrible!! I always thought it was a made up thing and people needed to MTFU. But after getting them and having to walk 50+ miles in crappy boots with weight, it ruined me for months. Couldn't run a few 100 metres without being in pain, and considering just before it I was doing 10+miles every weekend it was horrible.
I was told to rest it and it would be fine, I ignored this advice and kept running but used grass instead. Also cycling, do you have a stationary bike you could use for some HIIT?
HIIT is just awesome, for more reasons than just cutting. I swear by it, helped my running out no end and general fitness/health all round. I do it at least 2-3 times a week.
But it can be done with anything, you could even set up complexes by using the HIIT princibles.