I have this type of recumbent. I want to upgrade to hydraulic brakes, but every bike shop warns me about the issues that will come from attaching the brake levers in a vertical position. They say that it will catch air very quickly. Do I have any options? Maybe there is special brakes for this type of situation?
I can't speak for every hydraulic brake ever, but when I've done this I didn't worry about it, I just bought sealed brakes and put them on. I'm currently running cheap Shimano ones on my touring bike and have not had any issues, and in the past I used Hayes with similar lack of problems.
This bike I switched from cable to hydraulic after cooking the brakes on a downhill, and I haven't had any problems in about 5000km of riding since.
The brake will only suck in air if air is already present in the reservoir. With some brakes this may not be a problem. With brakes where this is a problem, you could take the rather extreme step of closing the reservoir while immersed in brake fluid (after carefully turning and vibrating to release air bubbles). No, I haven't tried, and yes it would be a lot easier if you could find a brake system that by design never has air inside the reservoir.
There are several models of recumbents that use under-seat steering and hydraulic brakes. My 2005-era Anthrotech trike used them exclusively, and I never had trouble with them. As long as they are installed and set up correctly you should not be worried. Remind the bike shop they can install the system with the handles horizontal first if they persist in being really nervous about it, then they can mount them as you need. :)