Help adding sub panel
My house is from the early 80s. I've done some light work on the main panel in the past but now I'm looking to add a 100 amp sub panel. I ran 1/0 1/0 1/0 2 wire and the sub panel side is easy. I'm having trouble figuring out how to add the wires to the main panel side though. Both the ground bar and neutral bar are full with 2-3 wires in each hole all mixed up on both sides. I added an additional ground bar that I'll move some connections to. My questions are 1) is AWG 4 copper enough to connect the two ground bars together 2) what do I do on the neutral bar side? The lug that holds 2/0 needs three slots so I'll be cramming even more to make space for it. I can try to move the ground wires to the right side proper ground bar but that will add more wiring and pigtails to an already very crowded panel. I'm assuming adding a neutral bar is not acceptable even though this is a main panel and ground and neutral are all bonded together.
Note that I had an electrician do analysis and the main panel can support the sub panel.
Thanks!
EDIT: Thanks for the helpful feedback. Most of the work such as transfer box was done before I bought the house. I did hire licensed electricians based on reviews (none were friends) and different ones installed the surge protector, an EV line (no longer visible, plan to pull it out of the sub), and provided quotes for other services such as close to 2k for sub panel. None mentioned any issue with the panel unfortunately. I wish one of them would have highlighted these are suspect breakers over 40 years old and you want to look into replacing them for instance. Yes load calculation was done (again by an electrician not me). The A/c and a jacuzzi we no longer use are off to the side and there are bedrooms with two breakers so I trusted the load calculations. Not a troll post.