If I might make a possible solution suggestion that on the surface "seems like" an easy-ish fix? I used quotes around that since it may be easier said than done.
Have you considered gating the maximum available popularity to hard timed multiple tiered events, with a bypass for label-signed bands? In this manner you could both slow down overly fast progress, make the struggle to make it as an indie band seem more real / gritty, and make there be some real visible benefits for signing up with a big name label.
Also, to prevent the huge "in your face" loss of profits from signing up with a label after being independent, it might make sense to stall the ability to "Release Single" in story mode until after the Launch signing and in open mode until after X years have passed or actual label signup.
In its place you could maybe open up a new part of the band site that allows people to purchase special release cd's of the band from the site using songs that have been recorded but not cut to a single or album yet. By doing this you wouldn't have to adjust the cd sales mechanics and could make a more realistic / slow buildup of sales revenues for early game indie bands.
Simultaneously might I suggest two extra after-gig random "reward" or "event" that increases the cash gains slightly or the popularity slightly depending on which of the two was triggered. The two new add-ons would be either selling a few recorded "demo" / "special release" cd's the band carried with them on hand to the event for extra funds, or gifting them out for extra popularity.
You could even use that hand-out cd event as your gate event for popularity levels. Maybe one of the people who received a handout "just happened" to have a friend or relative who will the following week let the band play in the lowest tier stage currently locked out by the popularity block. This would be a tentative offer though. Any failure to appear or a bad show result would keep the lock on, but a good showing would permanently unlock that tier and raise the max popularity limit.
That was all my "easy" suggestions for fixing this issue. Now comes the more complicated ones. But I think their potential game values would really make a huge difference in both game replay ability and realism.
Have you considered making the available gigs to play at each weekend on a semi RNG luck / popularity / band quality system? Where the factors for determining whether a particular gig is available that day is the gig quality (ie far more likely for a club gig to be available than an arena stage), partly on the popularity of the band, partly on the average of the 4 band member's total fame (ignoring writing values or music values since those have less draw power for getting people to want the band to come play - even music values only make the actual gig a success or a failure but have a small bearing for drawing in crowds if not famous yet). By making it so a band can't reliably twice a week play at their top value stage week after week I believe it would add more realism, help slowdown out of control fund gains, and add replay ability.
Basically this extra gig rarity code would make it so early game bands would even find the starting gig to be a welcome gig rather than a sure thing - just like that next new bar gig is for any up and coming hopeful band. However, a mid to end game band would almost have it as a sure thing available if they didn't have any better choices that particular day - assuming they wouldn't want to just skip such a low tier stage. On days when the band had no gigs to play they could still using the recording studios or hang out or relax together or just train like weekdays so I do not feel this code would cause any harm to a band merely slow down the out of control popularity and money gains.