Get hose pipe , feed around ubend and shove through as far as you can. (rubber gloves required !) Switch on.
Monitor for bowl filling up. - feed hose backwards and forwards if possible.
Alternative : If you cannot get the hose round the u bend, you could drill a small hole in the TOP of the soil pipe at a convenient point along its length then feed the hose pipe in there. On completion find a firm fitting rubber bung of some kind to block it again, (this needs to be secure and water tight.)
As a longer term fix, on this level pipe run you mention, is there any scope to get shims under at various points to wedge it up slightly at the toilet end and create a slight fall along this length.. ?