With a unit price at most 350 euro/ $450. Currently owning the Adam A8X and i really like them.
I'm not sure if I get you right: you have decent 8" monitors and want to downgrade to 4.5" cheapies, with the hope of maintaining the sound quality?
For one, you have to be prepared that the bass performance will be nothing like on your Adams. If you like their sound, consider a sub as well.
I have been researching monitors recently, but with more focus on 8" ones. The closest to your required size and budget I could recommend is the Neumann KH 120A which has a 5.25" woofer and is a truly excellent monitor.
Assuming you mean 'driver basket less than 11.6cm' and 'unit price' means a pair? If so the answer is no.
When I made a serious search for something suitable for desktop use which was unequivocally better in every way than M-Audio AV40 I couldn't find anything less expensive than ADAM A3X. You have probably already considered and rejected these as they now cost 420 Euro/pair. It was more than I wanted to spend at the time as well but I'm very glad I did. In fact I might even consider spending more on EVE 204, Focal CMS40 or even Genelec 8030.
Still don't think there is anything on the market that is as small and as good as the A3X for less money.
I can understand why the OP might want smaller speakers. I had a pair of twin 7" floorstanders. 240W. Listen much more often and for longer with more satisfaction on smaller monitors now.
Sometimes all that crashing and booming around the room gets too much. Like late at night, when you only want to follow the dialogue in a film, other people around, It's kind of easier with the furniture and making your living space useable and relaxed as well. Instead of everything audiovisual being centred around one regimented position you can have a room system and a personal system.
So having a discrete, elegant and pure sounding alternative is an attractive option. Plus since a 4" driver is easy capable of driving hard down to the ~85Hz crossover point you could build an awesome 100dB+ system by adding sub(s).
Although that might not be what he has in mind...so er...that's it.