Personally I found that a great way to improve at the game is to constantly learn new heroes. This gives you a great insight into how different heroes play at different stages of the game, and with different items, along with how they lane in different situations, and who they partner up well with; as well as keeping the game fresh and interesting (variety is the spice of life!)
For example - I kept getting beaten by Axe, so played a few games with him, did ok, and then watched the 'Purge coaches' video where he helped someone on Axe, which improved a) how I play Axe and b) how I play against Axe.
And this is something I now regularly do: get beaten by a hero/watch them played in a pro game, so I play one or more bot games depending on complexity of said hero (i.e. lion/lich - one game. Meepo/brewmaster - 3 or 4 games), watch a Purge video, and then dive into a real game. If I like the hero, I keep playing them, but if I don't, at the very least I've understood that hero's mechanics and playstyle, and over time, this will help you build a strong knowledge of the heroes, their builds, and item use.
If interested, my dotabuff ID is 98862191 "Cjeesebar" - you'll see I'm learning PA just now :) having just finished learning Bristle, LC before him, and WK before him; bit of Brew mixed in there too. Happy to take any questions on this approach.
What Dispenser says is absolutely true: every bot requires its own different AI, and some are better than others. Sand King being particularly famous for burrowstriking into trees and just chilling there. Maybe epicentering there. Viper bot and Warlock bot, in contrast, are regarded as terrors who nearly always win their lanes no matter what, and in some cases can win you the entire game by themselves.
On top of that, you can change the effectiveness of your bots simply by being on their team. A team of 5 bots can coordinate more effectively than, say, 3 bots and 2 humans. If a bot decides "we should fight here" on a team of 5 bots, it's pretty likely they will all reach the same conclusion and go fight. If a bot decides that same thing with a team of non-bots, then it's just gonna feed alone unless its human teammates are following it around.
That said, this:
I contribute to the team a very large amount in ways other than killing the enemy team (unlikely, especially when I try to play as a hard carry.
is entirely possible. Especially if you're receiving a lot of attention from the enemy team and you have other carries/cores that get farm while you're effectively making space (less likely with bots than in a normal match, imo, but still possible).
As for this:
The "medium" bots on my team are better than the "medium" on the enemy team, e.g. the enemy has bots with "9" skill, but the bots on my team have "10" skill to more than balance out my mere "7" skill.
I've never seen any indication that bots have intentional skill differences beyond "Passive, Easy, Medium, Hard, Unfair"
Best Answer
As of now there simply isn't any other way.
Last year's compendium had a few ways of leveling up your compendium through daily hero challenges and what not.
The community has launched somewhat of an outcry towards Valve in hopes of having a few ways of leveling up your compendium that doesn't include spending more money.
Give it a few days and you might see more ways of increasing your compendium level.
Edit: 15/5 -15
Compendium Additions
Added a fourth Challenge, which is always a Hero specific Challenge, and rewards completion with both Compendium Coins & Points.
Challenges are now available in Captains Mode, Captains Draft, Random Draft, Single Draft, and All Random game modes.
Ten Hero Challenge added to compendium, also enabled on the above mentioned modes. This year you can do the Ten Hero challenge 3 times for a total of 450 Compendium Points (4.5 Levels).
You can now destroy an Immortal to gain 200 Compendium Points for each.
Added back the Item Recycling system. You can now recycle 10 items for a Charm of the Crucible Jewel II and 25 Compendium points.
Added 3 Recycle Charm Achievements. Create 1 Charm, Create 10 Charms, and Open 8 Charms. Worth 50, 125, and 200 points respectively.
Added All-Star match voting (provides 50 Compendium Points).