Can't transmit more than 1348 bytes between two nodes

If indeed the supported maximum content length is slightly longer if the HTTP headers are slightly shorter (I’ve edited my response above), then you may be on to something.

Not my cup of tea either, but maybe related: Docker lowers interface MTU with 50 less than connected network, why? And as for a possible fix, Setting Container MTU in Swarm Mode may help. (Again, I’ve no idea.)