You’re basically wanting a large scale bonsai! It could probably be done but you’ll be fighting Mother Nature!

if you consider topiary .. there is no reason you cant train ANYTHING.. any way you want .. the usual caveat is.. no haircuts ..

you will probably have to start by IDing the graft location.. and of course.. never cut beyond that ...

otherwise.. and without a pic .. you should probably go in there.. and weed out enough structure... to get the canopy less wide.. and more weepy ... within the confines of the path ...

what i usually see with these type of trees.. planted on 3 feet form the corner of the house.. is they are left to their own devices for much to long.. resulting in a 10 foot mushroom shaped monstrosity that is rather out of scale to the house ...

if it had been trained since day one.. it could have been so much different ...

btw .. i just saw the 40 foot weeping birch in town the other day.. its incredible ... this tree does leader.. and continue upward.. for ever .. its the secondary branches that seep ...

https://duckduckgo.com/?t=ffab&q=weeping+puple+beech&iax=images&ia=images

and im not sure what version of weeping cherry you are referring to ... as there are the mushroom shaped ones... and the species which again.. is more of a tree ...

if the plant is glorious.. just move the path ... eh??? ... or prune a walkway thru the canopy .. lol .. [ i see on reread you reject that reality.. and want to substitute your own ...]

ken

https://www.youtube.com/watch?v=W8qcccZy03s

I just found a video about training weeping trees by tieing branches loosely to the trumk to maintain a tighter weep. ill try thst plus oruning out of the wayward branches.. You are right thst this should be done early. My trees sre grafted at the top.