Banners/Levelling

Nope. All other classes have been permanently removed from the game.

Sarcastic Comment aside, there are a whole bunch of servants coming out that aren't archers. You can use the all servants page on this site to search for a servant in a specific class you like then use stuff like cirnopedia to find banner dates. Rama is a good ST Saber with a strong crit skill and Extra Vlad is a solid ST Lancer with the ability to tank and support. In my opinion, go with Extra Vlad since he will be very useful in Shinjuku which is coming up in about a month or so.

You can even level up some of the 3 stars since a lot of them are good and can be good support when you get stronger servants.

Looks like this is more an Arts team than an Archer team. Get Tamamo (if you can) and you can make it really strong.