I'm thinking it is not going to be possible to solo all end game enemy fleets. Some fleets yes, but not all. I feel even something like a solo Onslaught, Legion, or Paragon is going to have issues against a double Astral enemy fleet, or a double Legion.
Also, the Electronic Warfare and Coordinated Maneuvers skills really reward deploying a full fleet. -20% to enemy range and +20% speed right from the start is good (just deploy 7 cruiser class vessels). It helps fighters against PD and it helps cruisers outrange capitals. And both stack with safety overrides or the ship-only skills. They're not as impressive early game, but late game they are stronger than the Gunnery Implant skill or Helmsmanship skill.
The following is roughly what I did on my commission-less run to level 40, with some tweaks from hind sight. I'm not saying its the definitive way or that you should play this way. But it is one way and you can definitely still be flying around fast and blowing stuff up as the major gameplay.
1) Buy a destroyer (enforcer most likely), outfit cheaply, destroy some ships in Jangala until you can fill your fuel tanks (either buying or salvaging) and have sufficient supplies and crew, and maybe 15 machinery.
2) Go after a 40,000-ish bounty, come back to Sindaria. Buy storage. Dump all weapons into storage, plus excess if any supplies. Buy fuel and supplies. Repeat.
A loss on this first outing can be painful, but after a few, you should have a buffer of a 50,000 credits or so. Keep that on hand so you can re-buy a destroyer in the case of a loss. Increase the buffer when you jump to Cruisers and then again to Capitals.
3) When possible grab multiple named bounties near each other, but even 1 generally pays for itself. Salvage interesting ships (I took things like Drover, Medusa, Falcon, Eagle, Dominator, Heron, Mora, Onslaught, Astral, Legion, etc). Restore them when able, or just shuck them into storage against future need. I've got things like Scarabs and Hyperions sitting in my storage which I haven't played around with.
4) When you've got a bit of cash store the fleet, keep a couple destroyers in fleet, and do a loop of the inhabited worlds to hit all the planets to visit black markets and grab new officers. Buy good weapons and maybe a ship you haven't salvaged. Every time I saw a rare fighter LPC, I bought it as well.
Sure I lost a ship here or there, which set me back cash wise briefly, but my character was gaining experience the entire time, and I generally had enough of cash reserve I could just fly back and restore it. I found the bounty fleet difficulties increased at about the right rate for me.
Supplies were not a big issue. Fuel became an issue at some point as my fleet was getting towards end game size, mostly because of the return leg didn't have a fleet waiting to be blown up for its fuel. At that point I decided to settle on Sindaria.
Leveling I did the following:
Technology first: +15% range, +10% OP, Navigation, Electronic warfare
Leadership second: 10 officers, +15% combat readiness for all, Fighter Doctrine, Coordinated Maneuvers
Combat last: +15% combat readiness, Defensive Systems, Level 2 into Helmsmanship (+10% speed) and Level 1 Evasive Action (+50% manuever).
No industry.
Fleet composition: Roughly half carriers. Half front line. Maybe a dram or two depending on fuel consumption.
Between fighter doctrine 1, officers with Carrier command 1, and Rescue shuttles, crew losses are nothing on fighters.
Officers: Aim to train them all as full carrier pilots at the start. Once you have 50% of your end game officer number as full carrier pilots (they have all 3 carrier skills at level 1 at least), fire excess partially trained carrier pilots, aim to train the rest as generic front line pilots. Fire and hire new as needed.
My current level 40 fleet has as its flagship a safety override and hardened subsystem Aurora (which with all the skills and a full fleet deployment has a base speed of 180, and 305 with plasma jets, and 4 minutes of deployment time). In addition, I have 5 Herons which get deployed every large battle (5 Broadswords, 5 Longbows, 5 Daggers), 3 Dominators, 1 Eagles, and an Onslaught. Plus 4 Medusa for dealing with small fry fleets or chasing down ships which retreat.
Typical deployment is the 5 Herons, the Aurora, and a Dominator. The Onslaught or Eagle come out depending on enemy fleet composition. Typically 155 supplies and provides the full 20% EW and Coordinated Maneuver benefits. 15 flights of fighters annihilate frigates and destroyers, and distracts cruisers and capitals nicely to let the Aurora flank. The Aura can also chase down annoying kiting ships. I can swap the Aurora for a Dominator, Onslaught or Eagle if its a particularly tough fight and I run out of endurance. Without the omni to front shield hull mod, I do have some minor issues with phase ships, but fighters or the beam Eagle seems to help with them.
I've been facing bounty fleets in the 250,000 to 350,000 credit range with this, and other than losing a cruiser once every 10 or so fights because I over extend, I find it works rather well.