Chris,
Quality rechargeable battery technology is anything but cheap. And no, you won't find LiON or NiMH batteries at standard alkaline D cell prices. If you could, alkaline batteries would be out of business. If you go to the nearest Sams club or Costco, they sell those Duracell multi-packs like candy, which is a testament to how their price vs. convenience point vs rechargeables are still acceptable. Lithium or NiMH batteries are very costly vs the initial purchase cost of standard alkaline D's but since they are rechargeable, if used regularly, will end up being far far cheaper in the long run.
As for buying a rechargeable "brick", if exists, you would likely be talking about something out of China. Here's the problem:
In the early stages of rechargeable battery technology, there was NiCD (nickel cadmium cells). They were great but their greatest shortcoming was that you had to run them all the way down before recharging or else you would lose capacity because those cells had a memory effect. If you regularly charged when 1/2 drained, you will eventually lose 1/2 the capacity. So chargers were rather simple. They presumed that cells were completely drained when inserted and the chargers would do timed charges (18 hours, etc.) then shut down. Then came NiMH which was a fantastic development and basically wiped out NiCD technology since gone was the dreaded memory effect. You can now charge any time, rather than needing to completely drain a battery. But because you can charge any time, a "smart" charger is needed to ensure that the battery doesn't get damaged from overcharging. It's still a terrific and viable technology today. Nowadays, it's all Lithium Ion cells. The advantages of Lithium Ion cells is that they have a greater power density for their weight. Unfortunately, the technology is also more expensive and requires even smarter cells & chargers due to these cells tendency to catch on fire.
Going back to why pre-constructed packs are problematic.... how are you going to charge it? Chargers today are intended for "sized" cells and their voltages. A pack would need a specially designed charger to be safe and reliable. I'm not aware of anyone that offers them yet. Todays cells have sensors embedded within and molded together into the packs to ensure that they do not overheat due to excessive charge or draw. Lacking these, I would be afraid to embed such packs into a boombox, especially if the charger is a 2-wire charger since that guarantees that there is no provision for sensor monitors.
Hacking alternatives? The safest and most convenient way to go in my opinion is to design a pocket to allow use of current tool battery modules. The newest cells are up to 5AH and 2 of them together would yield 10AH. 18v packs would be perfect. You can then simply stick them into the tool chargers when they need it and can be recharged in as little as 1-hour. No need to redesign the wheel when someone already did the R&D to produce a reliable system. Unfortunately, this is in no way, a cheap affordable solution. That's because the newest battery packs are probably going to run you over $100/pack so 2 of them will set you back $200+ and you still need the charger and to create a mold to make yourself a pack receptacle pocket. On the other hand, once you've made your own pack receptors, the packs & charger are all off the shelf common parts. Your boombox can run forever! You can of course use standard D cell rechargeables as chargers are available for them, the only downside being that 10 cells is a lot and you'll need to have multiple chargers available or else you'll spend all your time making one charging run. Remember, putting in an off the shelf pack, sticking them into a boombox that are often plugged in long term can be dangerous without a properly designed charger.