See pg 24 of your owners manual. Here is a link to download a owners manual for that rig.
The reason the clutch has lots of slack/play is the drive belt is worn which results in the clutching idler have to move too far to take up the slack. The more the clutch idler moves to take up the BELT slack the more forward the clutch/brake pedal will be for travel engauge disengauge. You might also have worn pulleys idle AND the top drive pulley worn on the sides allowing the belt travel too deep in the pulley.
It's quite a job to replace the drive belt and also properly inspect the pulleys. for example remove the deck, remove the front drive stack pulley or slide it down, carefully route the new belt and re-install all. After replacing this type drive belt I leave the deck off and test the drive BEFORE re-installing the deck. The mower will also have to elevated in the front. Quite a learning experience the first time doing such.
It's quite common for them type drive systems to have jack rabbit starts even with a new belt, might even be worse with a new belt.
Stay safe if under the mower. I use a chain hoist for such to make the job more user friendly.
Would be worth while to get an estimate for such from a shop.