hey!
so if i was you i would try and create both types of menus.
then i would use custom css to hide and show the menus based on which page you're on
https://laytheme.com/documentation/custom-css-styling.html#css-based-on-current-page
so lets assume your homepage has the slug home. and you have two menus:
.menu-1
and
.menu-2
then you'd do
//by default, menu1 is always shown, and menu2 is always hidden
.menu-1{
display: block!important;
}
.menu-2{
display: none!important;
}
// but on homepage, hide menu1 and show menu2 instead
.slug-home .menu-1{
display: none!important;
}
.slug-home .menu-2{
display: block!important;
}
this css is the basic logic behind how you show one menu on the homepage and hide the other. and on all other pages its the other way around.
but your classes you use will be different because you will need to hide/show a menu, a mobile menu or a button that opens an overlay. so you'll need to get comfortable with the "chrome inspector" for example to find the correct css selectors and write the css yourself.
also you're right you can't create multiple menus for mobile. for desktop you can have up to 4.
one way to get around this is to use "custom css & html" → "custom html at top/bottom"
in here you can hard-code some anchor tags and use custom css to style them. this could act as an additional menu on mobile.
all of this needs quite some knowledge in html and css but with some patience and learning you will be able to do it