There is nothing wrong with the sentence in the question—it's a normal way of expressing such an idea, and it's a quite common structure.
However, yes, it can be rephrased to remove the subjunctive and still mean essentially the same thing.
To make it natural, however, his name would need to be known:
？ A still living him would have supported the independence movement.
✔ A still living John Smith would have supported the independence movement.
While the version with the name is fine, and it is used on occasion, it's not as common as the subjunctive version.
Note two things here:
The subjunctive is part of a conditional, and is used naturally with it. You're not "mixing" the two.
Mixing verbs, when done correctly, is perfectly natural. Although learners might be told to not start off with mixing verbs, because doing so incorrectly is unnatural, once the language is understood, many sentences sound better when verbs are mixed. You might be confusing an initial prohibition against mixing verbs with the verb tenses used in conditional subjunctive statements.