There’s a few the advanced book club have read that look cool - I’m thinking of 容疑者Xの献身 and すべてがFになる. Having prior discussions to consult might help offset the “advanced” part. There’s also a mystery/crime novel nominated for the intermediate club (although it looks like it’ll be dropped before it wins a nomination poll at this rate…)
For ones I’ve personally read, I’ve really enjoyed the works of Edogawa Ranpo (江戸川乱歩) and Seishi Yokomizo (横溝正史) - their detectives, Kogoro Akechi (明智小五郎) and Kosuke Kindaichi (金田一耕助) respectively are about as 名 as 名探偵 get. I would definitely not describe the language as simpler though… especially for Yokomizo. Ranpo’s short stories (or boy detective stories) might be a good option, since the ones I’ve read are definitely page turners, but you’d still likely have to deal with some old-fashioned kanji usage. His work is comparable to Edgar Allan Poe (hence the name), and I think I read The Human Chair and other stories shortly after finishing my first novel and it was slow to read but I was very gripped.
There’s a lot of Japanese mystery novels though… for some other ideas here’s a wikipedia page and here’s an ebook site’s reader poll about their users’ 100 favorite mystery novels (I tried googling ”推理小説 おすすめ” which can find useful lists), I notice ビブリア古書堂の事件手帖 in there, which I’ve heard someone mention and want to read - might be lighter, book-themed mysteries? And I also notice on that list かがみの孤城, which there’s a book club of starting soon. I have no idea how crime-ish it is since the cover seems more fantasy, but apparently it’s enough of a ミステリー小説 for booklive, and the language is apparently easy and I’ve heard very good things about it.
Lastly - I know you’re looking for novels, but if you haven’t already, give 名探偵コナン / Case Closed a shot! I haven’t read any yet in Japanese, but I read a big chunk in English and found them to be a totally reliable parade of fun mysteries and I enjoyed it a lot more than I thought I would. It also has a bio of a famous fictional detective at the end of each volume, so you can source authors to check out that way…
Anyway, hope there’s some possible ideas in there at least! Good luck!