So, in light of all this, it appears that walling myself in my fortress is the only viable course of action. I can't understand it, as I've read community fortresses that raise dwarves to champion level after only a years' time and a siege or two, whereas my dwarves can't fight off cavern creatures with the best kind of equipment I can provide at the time. I want to be able to play liberally, but the game seems to be unwilling to let it happen.
If there's any way to remedy this, then I would stand another attempt. If not, I think I may very well just take a break and come back later on.
Well, of course there's a way to remedy it, those community forts don't have good militaries by accident, they have experienced overseers who figure out how to make the system work! Your dwarves will basically never get trained properly if you wall them in. The best training for new recruit melee dwarves is sparring (which they do best when training in 2-man squads) and/or killing invaders, preferably at first those which are already bleeding or stunned or fleeing after being peppered with bolts.
Try something like this
(1) Build two of the same weapon, two shields, 2 helm, 2 mail, and an armor stand by the time of the first migrant wave. Put 2 promising guys in a squad and let them train at the armor stand for a couple seasons. With only 2 guys they'll probably spar, which is the best way for scrubs to skill up.
(2) Equip a handful (4 to 6) of crossbowdwarves (xbow, shield, quiver, mail, helm). Assign them bone bolts for training & combat and copper bolts for combat. Never give any ammo for training only. Give an archery target or two but you don't have to actually put them on a training schedule (they'll use it in their free time). If you know how to use waypoints, you might want to have "at least 2" patrol a route atop your walls to get live practice shooting crows or whatever, and keep an eye for ambushes.
(3) Once your melee guys have some skill add them to a squad of ~6 to 10 dwarves. But put the training schedule on "at least 4 dwarves required to train". So they don't use the default mode of stand around and wait for every single guy to start the training. You could create a few more sparring teams, but eventually just switch over to big squads, it's fine. For best results group swords together, axes together, etc. to maximize value of demonstrations but this isn't critical.
(4) Look for opportunities to give your melee teams some live training on weak critters like coyotes. Look for combat but do NOT execute glorious headlong charge into battle until your guys have some skill, and add a full set of gear (default melee package + mail + cloak, for example). Lay out your fort so that the invaders have to walk past a simple raised platform or part of your walls with fortifications; use your xbows to weaken or break the enemy and only engage with melee to finish them. Against enemies who are better to fight close up like goblin archers, exploit chokepoints (a corner, or a 1-tile gap) to create "ambush zones" -- areas where your melee waits safely to mob the first enemies to come into sight. Put some weapon traps at these chokepoints with just a couple components, not to destroy the enemy, but to soften them up so your melee guys will have an insurmountable advantage.
(5) Once you get "ahead of the curve" -- i.e. your veterans can survive a skirmish, you have decent armor and good weapons, and a stocked hospital to fix up minor injuries -- you could plan on keeping the doors open and pretty much fighting off every siege. You should be rolling, as your newer recruits can fight more or less safely alongside the pros. Keep ramping up the recruiting though, you don't want to fight at a numerical disadvantage any time you can help it.
If you follow these steps then you should have ~4 each of melee legends and xbow legends after about 3 years. It is inevitable. Well, that's not true, you'll still probably fail, but the key is that you think about what happened and figure out what you did wrong or which part of the advice we gave you was junk, and you fix it. After a couple attempts you should have it down. If you're really not feeling like you're making any progress and it all seems totally random to you still, then maybe it really is time for a break.
From your comments you seem to think that a pack of "giant" animals is less dangerous than a goblin invader. Giant animals are huge and powerful -- their weakness is lack of dodge skills and armor. You exploit that weakness with, for example, xbow bolts, not by charging in an undertrained militia! (Invaders, on the other hand, are dependent on their skill and gear, so a copper-axe wielding goblin squad might be easy prey for your moderately trained iron clad militia. Use the Units tab to see if the goblin captain is a Master -- if so, he's more dangerous than the whole rest of the squad put together.) You will learn these things by experience, but i wonder if you are stuck in a rut of blaming the game for cursing you with bad luck, and so you aren't as open to experimenting and learning as you could be.