I know that my shop SEO in Shin Matsudo does but not sure what they'd charge. I've also heard that a lot of people are using a super strong double sided tape instead of the glue. You may want to find out if it's the new improved way of doing it. (seems easier if it's better).
The only time I've ever seen them over here (in Japan) was at my LBS... Kimura-san was gluing the second one onto the front wheel of a $15,000 bike - he was having some trouble getting it straight on the rim - not an easy job.
I don't think he likes doing it, because he probably doesn't have to deal with "tubular" tires very often - in short; very hard to come by, and will cost you a pretty penny, even just to get them fixed.
I'd take Pucci's advice, and just patch it yourself... Otherwise, look for a shop that can do it cheaper (Ask AlanW)!
Try Positivo in Meguro/Jijugaoka if its close. I've never been but have spoken to a few guys who swear by the place for repairs. The owner (Nagai-san) is an ex racer and spent some time as a mechanic for Fassa Bortolo. He's also one of Japan's commentators during TDF.
I'll 3rd or 4th the Shinjuku Y's Road being useless and unfriendly. The only cool thing is that you can park (hang) your bike right in the store, and the store itself is spacious and good for browsing.
I don't know if they are professional enough, but the Victoria bike shop (B1 of L-Breath/Victoria building) in Shinjuku (near Takashimaya) have been super helpful and friendly. They've given me good service. For example, took my bike in for a tune-up, and they just asked me what I wanted done (tightening brakes, check cables, clean up chain, adjust shifting), and then did it. All in 20 minutes. Cost? ¥520 yen. They have my loyalty.