WotBS WotBS starting at 7th level

I'm thinking of incorporate WotBS into my Age of Wyrms Eberron campaign, replacing the Ragesian Empire with either Thrane or Karrnath, and replace the Shahalesti with an adjacent neighbor to the selected country. (Elves vanished in my campaign.)

My PCs are currently at 7th. I'm debating if I should start them with The Mad God's Banquet or with The Scouring of Gate Pass. If I go with the latter, any suggestions on scaling it? What about The Indomitable Fire Forest of Innenotdar and Shelter From the Storm? Or should I chuck those two as well?

The first 3 modules do a good job of introducing the players to the complexity of the situation, with spies and agents from various nations and armies.

Scaling them would be, IMHO, a bridge too far if your intent is to complete the rest of the campaign arc. You would have to scale the entire arc.... level 27 for the finale?

You could, however, just jumpstart them with a 'this has been happening' montage and get involved in the Dassen situation at the level they are at.
What they would miss is the development of links to various organizations and people.. which means when those folks pop up later in the adventure you lose some of the cohesion and have to fit the 'new guys' into the trust framework of the NPCs.
When my group makes it back to Gates Pass they will be known for their exploits in the Fire Forest and Seaquen, as well as being known to key NPCs.

running WotBS as-is vs. heavily customized

I think it depends how much time you have available for creating stat blocks. Some people might think it's crazy to buy a commercial adventure and then spend hours and hours rewriting it to fit your own game, but personally I like to invest the effort to give my games that home-grown feel. The story of WotBS is top notch and I think it will come across well when transplanted into just about anyone's D&D campaign.

I would recommend replacing Torrent with an NPC that your players already know, to give them more motivation to get involved. Also, at 7th level they should be able to figure out how to sneak past the Ragesian army and get inside the city so I would roleplay that rather than glossing over it.

I'm afraid I don't know enough about Eberron to advise you on how to run WotBS in that world system. I would recommend downloading the free Campaign Guide PDF: it should give you enough detail on the factions and personalities involved to at least get started on integrating it with your existing game.