I like it better with the music but enjoy that it isn't hugely 'produced' - like the bluemoon podcast feels to me. It feels like knowledgable mates having a chat rather than a radio show. If it was me I'd have the acoustic guitar track play over your intro then stop when you're introducing the guest either with a fade or if the bumper was just perfectly timed with the end of the track - i.e. just have a 30 second distinct piece of music to cover an intro and some waffle then intro the guests. I think you've done similar in the past. You could have a different bumper at the beginning to keep the different type of shows feeling distinct.
I listen to a pod called Ten Junk Miles that plays some outro music as the conversation is coming to a close. Then they do the "see ya next time" but then carry on talking rubbish over a long fade. I like that as it feels like you're part of an ongoing conversation. It is a bit more ramshackle than how you guys do the pods but there are lots of similarities - i.e. similar lengths, solo shows and gang shows. BUT I know it is a personal preference thing and not having the opening & outro music won't stop me subscribing so do what you want :)
I like all the contributors you have as they all have interesting things. They are interchangeable in that they all do a good job but they all have a distinct voice - damo does the science, stefan cuts through the bull, howard does the pessimism etc. Basically you are doing good work