I think 10 items per screen is too many - I don't think you'll get a great read on the many items in the middle of the distribution. If you need utilities for all items, I recommend 23 sets of quints - then each respondent sees each item once (this is called a Sparse MaxDiff and it's been found to be the best way to handle large numbers of items). At 115 you're close to the limit of what you can do with a Spare MaxDiff.
Sparse MaxDiff produces excellent sample level utilities but as you imagine, the quality of the respondent level utilities suffers a bit (in an empirical study we published last year in The Journal of Choice Modeling, we found that respondent-level utilities coming from a Sparse MaxDiff were correlated at 84% with utilities generated from a standard 3x MaxDiff).
If you only care about winners and you don't care much about the quality of respondent level data you can do something called Bandit MaxDiff, which easily handles large or even very large numbers of items.