Thank you Bucklash, your words of wisdom were very useful. It seems I solved the puzzle... kinda.
Here's what I did:
1) I turned on the hidden new Joomla native SEF that gets rid of IDs in URL (and no - it won't get disabled with future Joomla updates - at least I've read so)
2) Set in SEBLOD settings SEF to Joomla native
3) changed a bit hierarchy of article categories, so they reflect manu item hierarchy. So for menu
Home page
Some menu item [Separator]
--Category1 [SEBLOD Search]
--Category2 [SEBLOD Search]
--Category3 [SEBLOD Search]
I created empty category 'Some menu item' and added categories 1-3 as subcategories
4) Set home page to Joomla native featured articles blog (thanks, Bucklash), which now redirects all the featured articles right where they belong.
The only minus here is I wanted to fully stick to SEBLOD mechanisms, avoiding Joomla native components.
As for 'Content > View', in case of 'featured articles blog' search type I didn't change anything - all the settings were set to default (SEF URLs - Inherited, Menu Item - Inherited).
Well, it's a workaround, but it works like I wanted it to, so... mission accomplished.