Skills in TMNT

OK.  I've decided I want to run a TMNT game.  But there are a few things about the Palladium system that I'm not in love with, and one of them is the whole % skill business.  I like a skill-based game, mind you.  I've kicked around with non class-based systems, and I tend to like them, but there are some issues with them.

The biggest ones, to my mind, are avoiding dead ends or useless skills, and maintaining a reasonable difficulty curve while leveling.

By the first I mean, there should be no useless skills.  And by the second I mean, you shouldn't have to have slipperier slime at higher levels.  You should just be better at dealing with slime.  But not so good that you never slip on slime - it's still more hazardous than dry floor.

I have also decided that I will make no major effort to address these potential issues of a skill-based system while reworking TMNT/Palladium.

Sooooo... how to deal with skills, if I'm not going to use a %-based system.  I want to use the existing body of TMNT skills, it represents a significant resource, and one that I'm not willing to throw out.  My inclination is to go with a difficulty-based d20 system. TMNT uses d20 rules already, so we're not that far off, and d20 is easy to convert into percentile chances, so it should be relatively easy to convert from a % system to a d20-based system.

I also want to rework the skill bonus structure, and the leveling structure to streamline things and hopefully build a reasonable difficulty curve.  I'd thought of using a "Target 20" idea for the rolling system, but I'm not sure it gives me enough flex on the math.  I'll be making a lot of decisions on the fly during the game, so I want a system that gives me lots of options.  I can do % chance converted to d20 in my head, and d20 is simpler for players.

My first thought on converting the TMNT skills to a base d20 system is to take the starting % chance on the skill, divide by 10 and round up.  That's the starting bonus for the skill.  Add a stat-based modifier and a dice roll and you should have a workable system...

But.  Doing that actually makes success in the skills much harder.  If you assume that 20 is the base difficulty, then each +1 on a roll represents a base 5% chance to succeed.  So taking a base 30% skill, making it a +3 modifier means that the player has to roll, theoretically, a 17 to succeed.  Which is really only a 15% chance of success.  Setting a base difficulty of 15 means that a +3 bonus represents a 40% chance of success.  A little closer to the starting point.  But it makes the math on the conversion harder.

Setting the base difficulty for most tasks at 15 works for me, the more that I think about it.  I expect characters at first level to have modifiers on most skills of between 2 (low) and 10 (high and/or exceptional stats).  I'm not sure yet if I want to have penalties on the roll, or higher difficulties for difficult tasks/conditions. Bears more thinking.  And I need to consider how I'm dealing with leveling.