Yes by all means petition for a rate reduction since getting blood out of a stone is impossible. However, if you apply for SSDI through social security and are awarded the benefit, anything you owe will be taken out of the back pay awarded to you by social security and part of your monthly benefit will go right to support at the original rate unless you re-file to have the support tied to your benefit. Another item of interest is that under SSDI, the children will also get money apart from your monthly rate and can be counted as support toward the monthly amount due.
As an example, if you pay $100 for each child in monthly support and social security sends them $75 per month, you are then liable for the remaining $25 and not the original $100. Support is defined as any source and since your disability provides them funds, it is coming from your account. Don't let someone tell you that you support is still $100 when SSA is sending them money. SSA for kids is deducted from the monthly support amount.