I'm going on vacation for a little over a week, so I wanted to post what I have learned about this game! I don't know if I want to run the whole game myself, but I at least want to share some cool tricks.
Here is a rough test run of the first level:
http://www.filespace.org/BagOfMagicFood/Tails_Adventures_U.mmv
Now, I think the real interest in this game is in seeing what you can skip, since it's an adventure. I think the only items you absolutely need to finish the game are Remote Robot, Remote Bomb, Napalm Bomb, Large Bomb, Mine, Anti-Air Missile, Extra Speed, Rocket Booster, and 3 Chaos Emeralds or so. I know 4 Chaos Emeralds is enough to withstand the mines in the low path of Lake Rocky without Extra Armor, and I know you can also withstand them with 3 Chaos Emeralds and the Spark, but I haven't managed it with just 3 Chaos Emeralds and not the Spark yet. Maybe when I get more time... So those Chaos Emeralds should probably be Red, Green, and Purple, since Red and Green aren't out of your way at all, and you're forced to collect Purple.
Now as far as speed-up items go, you can get the Speed Boots early on. Either backtrack from the Remote Robot right away, then go right back to the exit, or just exit, re-enter, and go back out the entrance, depending on whichever path is shorter; I didn't test yet. I don't know how much the Speed Boots help, though, since they only work on the ground and leave you defenseless. (The Sonic item lets you jump and attack while maintaining your speed, but it's much too far along--there's nothing essential in Caron Forest anyway.) I was considering getting the Teleport Device for levels where you just collect something and leave the way you came in, but it may lose its value due to an interesting glitch.
You see, when you collect an item with the Remote Robot rather than with Tails himself, you're still allowed to use your button-1 recall function to return to Tails while the item is flashing its name. This can have some strange effects on the scenery depending on where you use it, and it can even allow Tails to fall through the scenery and exit the level, since a pit counts as an exit!
There's another glitch that works against you a little bit, though. When you collect your first three items other than Chaos Emeralds, they automatically assign themselves to the next empty use slot, so you don't have to go back to your house to equip them. However, it stupidly also equips submarine items that you can't use as just plain Tails. So as you go through Cavern Island, starting with just the bare necessities of Regular Bomb, Remote Robot, and Remote Bomb, you can get the Mine, then the Napalm Bomb, but the Mine assigns itself to the fourth item slot, so the Napalm Bomb is stuck in your large inventory back at home, and worse still, the Mine still isn't assigned to the submarine yet. (You even have to equip the Vulcan Gun manually, even though it comes with the sub!) So you could either skip the Mine, get the Napalm Bomb, then backtrack to the Mine and finish the level for the Anti-Air Missile so the Napalm Bomb is equipped right away; or you could just equip the Napalm Bomb at your house, which is probably faster anyway. But if you're using Speed Boots, then none of this matters, since you picked your fourth item already.
So, go ahead and have fun with this game, and tell me if you come up with a new idea.