There are a number of problems associated with repacking "smart" lithium ion battery packs, starting with the "smarts" of them. Quite a few of them are programmed to fail after X cycles to coincide with the normal wear of the specified batteries, or if a fault is detected and write data to a bit of EEPROM or NVRAM so it's permanent. Even if you completely power down the protection board for any length of time before re-powering it with new cells, it usually won't reset.
Another problem is packs are usually designed with a specific cell capacity in mind and are tuned for that capacity. Using higher or lower capacity cells can cause undesired behavior, where the protection board doesn't agree with the real capacity of the batteries.
I found a guy that restuffed such a battery back in the mid 2000s with slightly higher capacity cells, and while it worked for a time, it had a pretty dismal lifespan of only two years:
He could have used low quality cells, or the protection board could have been charging the cells improperly, causing accelerated wear.
So while replacing the original ~1800 mAh cells with 3000+ mAh cells may seem tantalizing to get extreme battery life, I don't think it would be a great idea. Maybe if you could find a Chinese clone protection board that faked the required data and was just a dumb protection board that worked on normal lithium battery charge voltages, you could do something like that, but the laptop would still be very confused trying to estimate the battery life.
I think an external battery back would be a better solution that plugged into the DC in connector. It would be easier and less time consuming to make, rather than hacking apart an ultrasonically welded battery shell and restuffing it. You also wouldn't be limited to the confines of the battery compartment, you could make it as large as you wanted to, which gives a lot of room for less space efficient construction methods like solder braid if you don't have a spot welder.
