Maybe we should be thinking things a bit differently? Just throwing out some thoughts for consideration. This is not a big span bridge - 9m. This sounds like it is a small rural bridge. They don't have to be that heavy. Why no look at ways to minimize the loading - thin abutment walls and steel I-beams with a thin concrete deck. Use of lightweight aggregate? Perhaps abutment columns with soil nailed shotcrete walls behind - maybe an arch bridge where some of the weight of the bridge would be, in effect, lateral loads on the foundations which could be handled in the approach fill soils?
Foundations are a problem - I agree. If this were Asia, they would probably drive a whole lot of bamboo piles. What can be done to make the soils stronger in the upper reaches? If you can "stabilize" a box that would be under the footing, you might be able to look at a rather small footing. How can we do this? A regime of deep soil mixing - chemical stabilization - cement or lime - might be considered to provide a strong base onto which to place the footing. Electro-hardening (see T&P for discussion - the 1967 edition in particular) but this might be expensive - but has been used successfully since the 40s. One could also consider placing lots of small pin piles. Stone columns might also be considered.
We don't know how high the approach spans are - if high at all? Clearly, the approach spans will cause the supporting soils to settle - and will lead to lateral pressures on the abutment wall - although perhaps one could use columns instead of a wall with soil nails back into the embankment so support the embankment soil. This would minimize the lateral pressures on the abutment and hence the foundation. One could use geofoam for the embankment - virtually no loading on the founding soils so no settlement problems and no embankment influence of settlement below abutment foundations.If groundwater is a problem, you could use geo-tubes (can't remember off hand the trade name) - they are basically pvc tubes standing vertically, tied together - allowing water to go "up and down". One might be able to excavate a couple of meters of existing soil and replace with the geofoam - to get no added pressure at all. One could also use shredded tyres for lightweight fill.
We don't know what the "scour" potential of the river/stream is. Is scour a problem? Does the original bridge have a problem? If so, one might consider placing a rip-rap blanket up and down stream large enough that if scour occurs by the time it reaches the foundation, a wall of rip-rap will have developed.
This is an interesting problem and sounds like a lot of fun. There are ways out there that might be done relatively cheap. I hope that some of the thoughts above might get one to think that there are other "toys" out there rather than box "culverts", etc. Good luck.