For when/if someone actually does this, since I have both games, I know it's possible to do it without link cables.
At the end of the game, you recieve a password, and that password activates certain events should you use it to start the other game. It's a long process.
1. Beat Seasons first to get a password.
2. Use the password to start a game on Ages.
3. In Ages, there will be people who don't apear normally, and they will give you a password. Copy that password down.
4. In Seasons find someone to give the password to. They will be new too. They will give you another password. Copy it down.
5. Give that password to the first person in Ages
6. Beat the game with extra bosses.
In a speed run, you would condense 3-5 into seconds of password entry. You'd probably only bother with the sword, ring, and mabey the shield or ringbox ones.
Beat the Heroes cave ASAP to get the Power Ring L-3, which gives you 2.5xdamage. Or you could get it from the ring password (get the ring, put it in Seasons, get the new Ring Password to use in a faster Ages time attack).
You'd also want to keep password runs seperate from non password runs, what with those bosses...