In my opinion, synthetics are far superior, and the attachment to dino oil is simply a case of outdated knowledge or a desire to minimize costs. Most of the arguments against synthetics are misconceptions. The real issue, as you realize, is the level of particular anti-wear additives such as zinc and phosphorous. If dino oil is missing these elements, then it's even more of a catastrophe than synthetic oil missing this stuff. Whatever oil you use, make sure it has adequate levels of these substances.
Almost all modern ("SM") rated oils are low in zinc in order to meet the SM rating, which calls for low zinc in order to preserve emissions systems. So if you get a synthetic with good zinc levels, you'll be ahead of any dino oil that has the same.
Some of the common claims against synthetics -
1) causes leaks due to seal shrinkage on old seals - only the original synthetics in the 70's did this. Since then, all synthetic oils have compounds to prevent seal shrinkage.
2) causes leaks due to detergent effect on gunk and deposits - possible. If the engine is old and neglected, and is actually "sealed" with gunk, the inherent cleaning effects of synthetic oil can clear off the gunk and "cause" a leak. I think the effect of this is overrated though, as I started using this stuff on an A-series with at least 40,000 miles on it and here I am, 30,000 miles and 4 years later, and NO LEAKS, believe it or not. Leaks are mainly caused by bad seals and gaskets, not oil!
3) bad for transmissions that share engine oil - I believe this is a confusion with motorcycle motors that run wet clutches. In some of these motors, the extra slickness of the synthetic could interfere with clutch operation. As Minis run dry clutches, it's a non-issue. I don't see how a fluid that is more resistant to shearing and breakdown would be bad for a transmission, which has much more friction than an engine. Obviously, many motorcycles run beautifully on synthetic and in fact it's recommended on a lot bikes like the big air cooled V-Twins, that run really hot and really benefit from the greater heat tolerance of a synthetic oil.
Basically, while dino oil is perfectly adequate and fine if changed often enough - there is no doubt to me that synthetic oil is superior in every way to conventional oil. Just like synthetic rubber is vastly superior to natural rubber (though not to as great as extent.)
As I mentioned elsewhere, I use Redline synthetic which has retained high levels of zinc for wear protection. (I understand Redline no longer carries a API designation such as "SM" because they won't lower their zinc content to meet that standard.) Many of the common Mobil 1 formulations do have lowered zinc levels since they are SM rated, so you'll want to research those and use the additive if they are lacking.

Some years ago I worked with an expert in lubrication technology (who worked for the Government and not an oil company). When I asked him what was wrong with synthetic oil he had a simple answer... its too damn expensive. Otherwise it outperforms "normal" oil in pretty much every aspect. Remember though that protection levels are directly proportional to viscosity. Most synthetics tend to come in lower viscosities than the other sort. The good thing is that this is sort of OK because they have a more film strength. However, you really do want to try and match numbers. 0W30 is not good enough.
I used to use Shell 10W60 but you can't seem to get that anymore so now its Castrol 15W60. Another good thing about synthetics is that they can produce good film strength without additives so they tend not to "wear" out quickly like ordinary oil when the long chain polymers additives (that provide the high end viscosity numbers) get chopped up.
I've been running the same engine and gearbox since 1992 for commuting and the odd competition. I had to replace some gearbox bearings because I left old oil (I didn't think it was that old) while the car was in storage for 4 years. Other than that I still get over 1500 miles to the pint. Not bad for a mini motor with a few leaks...
Put me firmly in the synthetic fan club.