Just to follow up, my attempts to get vimtex to work unfortunately were unsuccessful. However, along the way reading neovim plugin docs I started to figure out the difference between neovim and vim and was able to get things working via the following process:
vimtex works perfectly on neovim (in fact, the main developer uses neovim) and is very well documented
texlab (the latex lsp server) also does build and forward search (although there's a small bug at the moment)
Oh, and backward search needs neovim-remote (\o/ mhinz); just use nvr --remote +"%line" "%file" as backward search command
https://github.com/lervag/vimtex/blob/5d1335d095d11f48a6744f...
(the vimtex dev uses Zathura, so that may be an alternative viewer to look into)