Instead of drawing one card per turn from a common pile and starting with six cards, instead start with four or five (I haven't worked out the details at this point). Also, deal a "personal" draw pile of 20 cards to each player. At the end of your turn, draw back up to four or five cards. When your draw pile runs out, you no longer draw cards. When your hand runs out and there are no cards to draw, your turn is skipped. You *must* play one card during your turn if you have one or more in hand.
The idea is that you can choose how quickly to move through your deck, allowing for more combos, etc. There may be a couple of action cards that would affect this, but in general it seems like you'd move the game along a *lot* faster and have more control over your resources. Clearly, burning through your cards quickly while others held onto them would mean no responses could be played, so there would still be an element of strategy in how quickly you played through things, but it wouldn't punish playing combos as much as the current mechanism does - My estimate is that with a fixed set of 15 turns and 25% of your cards responses that you play defensively, that means you play on average one card per turn, not very interesting.
There is no way, in my estimation, to fix the solitaire game other than to automate the Phantom Player so that the AI is managed by a computer rather than forcing the player to go through that tedium, although you couldn't use my variant with the solitaire game in any case.
Please let me know if you try this and feel it helps. God knows the game needs it.