I have tested combining the use of basal insulin and using a pump for meal boluses. It works fine.
The post-workout lows may be because exercise increases the absorption rate of the insulin that is used by a pump. Since a pump uses rapid insulin, exercise can increase the rate your body is putting it to use. Basal insulins are not affected by this in the same way.
Lantus uses higher order aggregates of insulin hexamers, and Levemir binds to the albumin in the blood, so their rate is less affected by exercise.
The only downside to this approach - once you take a Lantus shot, you can’t stop it or reduce it, you gotta ride it out.
An alternative might be to more aggressively adjust your basal rates post-workout.