Okay, I'll chip in - as I was one of the silent 118!!!!!
Mainly I was quiet because I thought someone with a definitive answer may be along, but I'll throw in a few ideas....
Firstly, does the vibration come in at a certain speed (mine does it at 55mph, but disappears at 62mph) - I know it is down to wheel balance as I changed the wheels for some from Angies car when I was trying to see if her wheels were buckled when I had the rear hub issues 3 years ago)..... but mine is so minor that I am not worried, and it also helps me regulate my speed.... if I stay at 55 in a 60 limit, I get no vibration, but if I stray higher, I notice.... and it clears on the motorway anyway.
Anyway, you don't care about my issues - you want to sort yours out.
So, as Mike says, take it back
No disrespect to you, but how I deal with it is somewhat different than how you do stuff...... I would swap front wheels for rears and see what the difference is, to try and narrow it down..... then use other wheels from the garage until I either eliminate the issue (and identify the problem component) or work out that it still happens whatever, so it is a problem elsewhere.
So, if it didn't do it before, but does now - it is down to something that has changed...... and the obvious answer is wheel balancing. The unfortunate reality is that tyre fitters are usually allocated (officially or otherwise) a time to do a job - and as the Elan takes a bit more care (and thus, time) to jack it up and remove the wheels, they may need to hurry up the rest of the process.... back in the "olden days" we would drive to the tyre place and simply wait in the queue until it was your turn, and it took as long as it took - now it's all done on appointments and time slots.
Balancing is an easy thing to do, but without 100% care, it can be done wrongly - or, more accurately, incompletely.
Tyres are inherently 'unbalanced' to allow for the weight of the valve assembly - a tyre will have a 'heavy' side (marked with a blue dot on a Yokohama - no idea on a Conti) which should go 180 degrees from the valve...... on modern tyres this weight difference is more pronounced as modern cars have the TPS system inside the rim to add to the balance problems.
Anyway, the balancing machine should be set to rotate at 150-200 RPM, while a 60mph road speed is about 660 RPM - but as it is computerised it *should* allow for it.... BUT..... it will only allow for the tyre to be balanced 100% at that speed. So, if the machine isn't correctly calibrated, it will never be accurate at all speeds.
Also, many fitters will use the machine, whack a weight on where it says, and call it a day (and most of the time it is close enough) - what they should do is run the machine again, check the balance, then stop it, release the wheel, rotate it a bit, tighten it up, and run it at speed again to check. Maybe adding smaller weights to adjust things.
A 'great' fitter will do all this every time, and even trim weights down by a couple of grams to get it 100% right....... but it takes time...... so most don't bother unless the customer returns.
The tyre place have the ability to do it right, but not often the inclination - until they have to.
It could be a simple matter of a weight being 'close enough' to what is needed, or it may not be stuck properly to the inner rim (assuming that have used self-adhesive weights).... also, they may or may not have fully removed all the adhesive from previous weights which may attract debris and change weights.
Either way, if it isn't right - back it must go
) I was getting some vibration through the steering which I hadn't experienced previously with the Toyos. 
