Have any prominent Christian Intelligent Design proponents discussed the issue of a potential infinite regress of intelligent designers?

This is not an area of focus in scholarly publications on Intelligent Design.

Scoping Intelligent Design

Intelligent Design is not a viewpoint restricted to Christians. It can include Jews, Muslims, and other faiths. Neither is Intelligent Design a viewpoint restricted to those who believe in God.

Though many proponents of Intelligent Design do believe in God, a person who is agnostic on the subject of God can still look at the evidence in cells, conclude through abductive reasoning that the best explanation of this evidence is that there is a designer, and remain uncertain as to the identity of the designer.

A Christian may believe the designer is God, a Muslim may believe the designer is Allah, and an agnostic may believe the designer is of an advanced extra-terrestrial race. DNA, developmental gene regulatory networks, epigenetic structures, and mechanical systems within cells provide reason to believe in an intelligent, powerful designer, but these alone do not provide the characterization of the designer--or the designer's intentions--that are a hallmark of religious texts. The common Christian view is that character & intentions are known because the Designer chose to reveal them.

Intelligent Design studies what the designer has revealed through the natural world¹. Theology studies what the Designer has revealed through authorized representatives & texts.

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Infinite Regression

Philosophically there is nothing inherently wrong with an infinite regression. Infinite regression/progression is common in theoretical models, and although we may struggle to wrap our minds around the concept of infinity (but to be fair, the quantum realm isn't exactly intuitive either), nothing in the evidence of design in cells validates or falsifies an infinite regression.

A commitment to materialism, or a specific set of theological views, may pose a problem for an infinite regression. But without the input of outside information, biology-based design arguments themselves are not going to exclude infinite regression or an unmoved mover.

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Conclusion

Thus, the answers to the OP's questions, strictly from the discipline of Intelligent Design, would be:

Have any prominent Christian Intelligent Design proponents discussed the issue of a potential infinite regress of intelligent designers?

No, because this goes beyond what can be inferred from the data.

Do [ID proponents] find an infinite regress of intelligent designers problematic?

No. Proponents of Intelligent Design who wish to address this question would do so through the inputs of other disciplines, not through Intelligent Design. From the discipline of Intelligent Design neither the unmoved mover nor the infinite regression can be affirmed or denied.

Is there a way to solve the infinite regress problem without resorting to Creationism?

I see at least 2 possible ways to do so:

• Affirm the infinite regression
• Accept the reality of an unmoved mover without taking a position on specific theological claims about the unmoved mover.

Appendix--entropy

One of the agnostic approaches to this question is to assert that although life on earth must be designed, it may be that there are life forms elsewhere that developed along a different path and did not need to be designed. If those life forms advanced sufficiently to experiment with biology, such life forms could be the designers of life on earth.

We have to be careful with what is meant by "complexity"--which could be a post all its own--but because the universe tends towards entropy, it is unclear why we would expect the complex to come from the simple, rather than the other way around. I contend that there are no clear examples of an entity designing something more complex than itself.

E.g. beaver cells are more complex than beaver dams, spider cells are more complex than spider webs, human cells (& minds!) are more complex than any machine humans have (yet) produced. The world of AI is...complicated. It may yet disprove my suggestion, but no software of the present is as complex as a human.

In the realm of design, then, "Complexity(ID1) >= Complexity(X)" is true for every design available for evaluation. "Complexity(ID1) < Complexity(X)" appears to be devoid of empirical support.

^{1 - specifically biology. Teleological arguments from the fine-tuning of the universe create a much greater problem for extra-terrestrial design theories, but cosmology is outside the scope of this post}