Alternate Itineraries since Mt Rinjani is closed?

You could easily travel from Bali to East Java overland, visit Ijen and Bromo, and get a bus back, all in 5 days or less. Java is actually much closer to Bali than Lombok.
Of course you must travel back and forth, though you could fly back from Surabaya if you prefer.
You could also climb the volcanoes of Bali, but they are less spectacular and kind of ovepriced tourist traps.

Thanks! Since I am traveling alone, do you know of any good tour companies that I could join a group to do this with? I prefer being in a group so I have people to hang with, but I've checked out a few companies that only do private tours of 2 or more people.

Most people do this either by public transport, or on tours starting from Yogyakarta, so I can't recommend anything from Bali.
Mind you, once at Ijen and especially Bromo, you certainly won't be alone any more...

For Ijen starting from Ketapang harbour you can join a group tour, about IDR175K not including entrance fee. For Bromo starting from Malang it's about IDR600K including entrance fee. There are direct buses, minibus shuttles & train from Banyuwangi to Malang.
For all-inclusive group tours starting from Bali or Ketapang harbour to Ijen & Bromo I have no recommendation.
PM me if you want more info.

We have exactly the same problem (5 spare nights), when are you going? I'm currently looking into the option to fly to Surabaya from Bali, do the 3D/2N trek to Semeru summit via Bromo and either fly to Lombok directly or squeeze in Kawah Ijen before flying to Lombok.

Oh! Yeah, that sounds pretty similar to what my new plan is. I would be doing that August 16 or 19 depending how I rearrange my trip. I am traveling solo though and struggling to find tours that aren't private. How about you?

If you are desperate to do it all as a group tour, and can't find one from Bali, you could consider flying to Yogyakarta and starting from there.
To make it more worthwhile, you could take a day tour to Borobudur and Prambanan temples from there as well.
It should still be doable in 5 days.

Just to throw another option out there, why not look at Sumbawa?