Could ammonia displace a chloride in dichloromethane to form a methylammonia? If so, given enough reagents and time, could this be used to make a 3D structure comprised of nitrogen bonded carbons, and carbons bonded to nitrogen and hidrogen?
If the reaction with methanal does not yield your product, DCM, being less reactive, won't as well.
I cannot point out why the reaction stops there, but from Wikipedia it seems that methenamine can be easily converted to a quaternary ammonium salt by simple alkylation.
Furthermore, your product has a problem: if the nitrogens did become quaternary ammonia**, your structure would collapse due to Coulomb repulsion caused by the positive charges.
** I'm not a native speaker, but if equilibrium plural is equilibria, I think it is reasonable for ammonium plural to be ammonia.