Lux-Perpetua the H1-A can handle triples in series well at least at 2A maximum output, Jensen567 did such testing.
For what you want the TPS61088 boost controller is probably not adequate, too limited I think.
For succesfully driving an XHP35 the Monolithic Power Systems MP3428 (used in the H2-C, see this Jensen567's quote) is a much better choice. And now that we're here, the MP3429 would be an even better choice as we usually want more current. ;-)
Cheers ^:)