You won't find any handles that will give you clearance for blinds, unfortunately. It's not the handle that's the problem, it's the spline stem. Even if you had a handle that folded down as low as it could possibly, go, the spline stem would still get in the way of the blinds.
The only solution is to mount the blinds in a way that gives way for the operator.
Sure, a good T handle would be our 39-102. This should be fully compatible with the existing parts.
For the operators you show in your photos above, you can use the 39-107 cover.