Unfortunately, you seem to have picked the most messed up crankset Shimano makes. A FOUR bolt crankset that uses 110/74mm bcd. Until now I had never heard of such a thing. And looking around, there are ZERO chainrings available for this goofy size. So it looks like this crankset is stuck with the factory 50-39-30 configuration. Maybe the simplest and cheapest solution is to just replace the crankset with a Sora triple. See following links. It has a 74mm bcd FIVE bolt inner chainring. You can cheaply and easily put a 24 tooth inner ring on it. Then your low becomes 24x32. Should be low enough. You could also try a 11-34 cassette. Get a little lower and probably not much chance your rear derailleur will not work with that. If you go nutty and try a 36 rear cog, then your derailleur hanger my not be low enough and the rear derailleur will not fit underneath the 36 cog. So that will not work. 34 most likely not a problem. But you have to try it to know. Going with a mountain bike triple crankset will allow you to get a 22 tooth inner ring. Little lower than the Sora 24 inner ring. Not sure it makes much difference. Safest is to go with the Sora. Positive it will work 100% fine. 24 inner ring is low enough. I rode the Dolomites and Alps with a 24x32 low gear and four panniers and other bags.http://www.jensonusa.com/Shimano-Sora-FC3503-Triple-Cranksethttp://www.ribblecycles.co.uk/shimano-sora-triple-3503-9spd-chainset/pid=19642?currency=USD&location=USAhttp://www.genesisbikes.co.uk/bikes/adventure/adventure/tour-de-fer/tour-de-fer-20
My current touring bike has Shimano 105 triple STI 10 speed shifters, Tiagra triple front derailleur, and 9 speed Deore rear derailleur. 10 speed cassette 11-32. Shifting is 100% perfect always. Crank is old 7 speed Deore with TA 44-33-20 rings. Inner ring is down to 20 through a Avid Tri-Adaptor thing that allows me to replace the separate spacers and bolt on a 58mm bcd inner ring. Perfect shifting always. Doubt there is enough room to allow the rear derailleur to get under a 34 ring on the cassette. No way in He-- it could ever fit under a 36 ring. Rear derailleur hanger length will decide if your bike can fit a 32, 34, or other rear cog. 32 cog always works. 34 may or may not work. 36 is very doubtful unless the bike was specifically built to work with that pie plate.