I would follow Guinne's suggestion - seek legal aid on DC's behalf and judicial review (high court action) against your LA. Afaik, there are two organisations with a franchise for legal aid in education law in England:
Simpson Millar - a top ranked firm of education solicitors, who also have a franchise for legal aid in community care law (useful in cases where social care and education are intertwined). Social care can pay for transport for SEN students, where they have a personal budget or just pay it generally.
The Coram Children's Legal Centre
Its means tested, but as the legal aid is for DC, who assuming he only has his benefits, and no other assets or income, will qualify. You act as his friend in litigation, as it is unlikely he will be able to instruct the lawyers himself. Sometimes a pre-action protocol letter (you will have to pay for this yourselves, I am afraid, but its the first stage - after that, everything is done on legal aid) from a firm of solicitors is enough to spur a LA into action. LAs do not legal aid, and the thought of the legal costs of a high court action may concentrate their minds.
Realistically, paralegals do most of the preliminary work on an education legal aid case, because legal aid rates are so low - but they are working under supervision of solicitors. If it got to the high court, a barrister would be used.
If you speak to one of the legal advisors at either of the above organisations, and they agree to take on DC's case, they will tell you that you have to go through the Civil Legal Aid gateway - they check DC's eligibility for legal aid, and then put you back in touch with the legal advisors.
The chief executive of SOS!SEN is Eleanor Wright. She was always ranked for years, by the Legal 500 or Chambers, as one of the top education solicitors, until she went to work for SOS!SEN. I believe that sometimes she will do a pre-action protocol letter for parents, cheaper than the education solicitors above. (I have only heard this on the grapevine, as I went to Simpson Millar myself, last time I had to seek judicial review against my LA).
(She did a pre-action protocol letter to my LA on behalf of some other parents about SEN transport)
If DC gets DLA/PIP, then he can claim ESA as a disabled student - unless you live in a universal credit area. This means he does not have to go through a work capability assessment. I believe the basic rate for on ESA support is £110 per week - so it is worth giving up child benefit to claim ESA. You can claim carer's allowance, which is about £62 per week. However, I do not know how it impacts on child tax credits.
IF DC gets DLA/PIP and ESA as a disabled student, then his school/FE college can claim a bursary worth £1,200 per year. Its up to them how they spend it; but they might for instance buy him equipment like a laptop or I Pad with software to help with his learning.
As for people who say SEN students over 16, can never get transport - DD got her transport paid for until she was 22. Education paid for her through school. It was accepted that her specialist FE college was the only placement that could meet her SEN, and as Guienne said, the LA had to pay for the transport, because otherwise she could not access her education and she could not possible use public transport. Education would have paid, but Social Services offered to pay (we never had direct payments or a personal budget, as I don't want them), so I took Social Services up on it.