I was about to say that I just made a board like that recently, but then I remembered that recently for me is 10 years ago.
The advantage of converting the signal the way you suggested is that you would still be able to generate the 44MHZ when you need to.
An easier way to convert to 24MHZ though would be to rewind L201A. But then you'd need new marker crystals or feed an external signal generator into the external marker jack.
Given how inexpensive the 415 generator is I picked up two of them hoping to try both methods. But, I just have too many projects. That's not bad though since I won't be bored once I retire.
John