Mounting larger bumper to Shasta and/or bike rack-need help

What did you end up doing? 

I'm newbie to Shastas but I have a great deal of experience towing with bikes and kayaks and can impart some knowledge here. 

First, most, if not all, bike racks state on the packaging or instructions that they are not meant to be used on trailers.  Yes, people do it.  But the probable reason is that there is a lot of bounce back there!  I know of two instances where people had the metal or pins shear and lost their or drug their bikes and racks.  And one was an expensive name brand rack that the metal sheared into at the receiver entrance.  Scary.

I have a receiver on my teardrop and I did try carrying my bikes.  I had a problem with sway, because the rear weight was more than the tongue weight.  A lot of people do carry just one with no problem but I would strongly recommend if you do this to get a hitch tightener to eliminate as much play in the receiver bar as possible.  There are a couple of kinds, some people use the U bolt kind, but I prefer this hitch clamp, ecx.images-amazon.com/images/I/31LDlmTXAkL._SY300_.jpg  as do my friends no who had the U bolt.   (I use this on trailer hitch and extender bars, too,)

The best alternative for me turned out to be a dual hitch extender.  I put my bike rack in one, use an extender bar and put my trailer on the other.  I traveled 10,000 miles and no shear or wear (used the hitch clamp), carrying 2 bikes, I even traveled 1000 miles with four.   Dual hitch extender:    www.amazon.com/CURT-Manufacturing-45792-Receiver-Extender/dp/B00371VLAC/ref=sr_1_1?ie=UTF8&qid=1383869125&sr=8-1&keywords=dual+hitch+extender 
I too, would like a receiver on my Shasta.  I used the one on my teardrop for my cargo rack.  It also makes a nice place for TV antenna

Somewhere I have better pics of my rig, but here's one:

cdn.vanillaforums.com/littleguy.vanillaforums.com/FileUpload/e7/5d8232eb8eadc8ca605bab0ce21aab.jpg

My old friend Bob (who gave me this nickname, and whose girlfriend it was with the table full of BB gun targets from the man glamping thread) bought an old van-based Class C motorhome when he decided to move to Florida. He welded a long, wide steel U-channel on top of his rear bumper to carry his Harley from Maine to Florida... He made it, too. I stopped by while he was building it, and he told me he had just finished cutting some metal underneath with a skil saw and one of those woven metal-cutting blades. When he shut off the saw, he heard this whooshing noise... Turned out he cut right through a propane line. I still can't believe he didn't blow up with the absolute shower of sparks those blades throw out.

We bought a Curt front mount hitch receiver to carry our bikes on the front bumper so that we can see them, and are not continuously wondering if they are still attached to the rear of the trailer. Our rear bumper on the trailer needed gussets welded on to streghten it, as th ebumper bent when we put stabilizer jacks under the first time we went camping. We are still going to mount a tire carrier on the trailer's bumper but the weight and logistical problem of bikes AND spare time led us to the front mount solution.