I think there's a relatively low-tech way of showing blocks on the homepage in a different order, based on whether it's viewed on desktop or mobile. We could use CSS "flexbox" properties to flop the order based on screen width.
When viewed on desktop widths (> 1024px), the main section could be displayed like this:
Welcome section
----------------------------
Repeat of left nav links
When viewed on mobile widths (< 1024px), the main section could be displayed like this:
Repeat of left nav links
----------------------------
Welcome section
This is not my area of expertise anymore, but I'd be willing to try to talk through it with someone, if the devs decide they want to try this.
(Here's a quick tutorial that illustrates this idea,
)