Good news: Both are fine and mean the same thing! Rich though he may be, he had no personality. Happy as she might be with her career, she wishes she made more money. I'm visiting my godfather next month, boring though he might be. Hot as it might be, I'm still going to wear my new jumper! Hilarious though they might be, my friends aren't the most dependable of people.

As a native English speaker I would use both. I don't see any difference in the meaning.

Thanks Michael 🙂

I can't see any reason why you can't use your version. Ngram viewer agrees .... https://books.google.com/ngrams/graph?smoothing=3&corpus=26&year_end=2019&content=expensive+as+it+may+be%2C+expensive+though+it+may+be%2C+&year_start=1800&direct_url=t1%3B%2Cexpensive%20as%20it%20may%20be%3B%2Cc0%3B.t1%3B%2Cexpensive%20though%20it%20may%20be%3B%2Cc0