I tinkered around a bit with the profile options. I found that by enabling "Proxy Maximum Segment Size" on the external side of the connection, the packets sent from the LTM to the client were full - 1380 bytes. This is with Nagle's algorithm disabled, and was my desired effect.
I took tcpdumps on both sides of the LTM. The Proxy MMS setting resulted in the LTM informing the webserver that the MSS was 1380 - matching the client. But to my surprise, the webserver seems to be sending full-sized 1380 byte segments, instead of splitting them into one full and one small segment like the LTM does.
Not sure I understand why, but this setting seems to have done the trick.