Any thoughts on having a ‘traditional’ stiff walled Marathon Plus 1.75 on the back and a 2.00 Big Apple on the front to act as a shock absorber (a bit like a hardtail MTB)?
Interesting thought. You can tailor the roadholding and handling of your bike via tyre parameter and operation choices for sure. In fact, those should be your initial attempts to gain control of the bike. Compare that normative case to what most cyclists do first: consider a softer saddle, a mechanically sprung saddle pin, mechanically sprung front and rear connections between the frame and the hubs. Actually, working through the tyre possibilities gives you the most bang for the buck.
I knew about all this from motor racing but it was reinforced for me when a Royal Dutch Gazelle I bought sight unseen turned up with a recent relatively strong cable disc brake at the front and an elderly design of hub brake at the back. This in fact gave me a sort of anti-skid braking, which I considered a safety measure as I'm a social rider, carrying on conversations, always distracted by whatever there is to see, therefore liable to slam the brakes on hard rather too often, which is in any event how I ride even when alone. The equivalent of this, and relevance to our discussion of basically sidewall stiffness/tyre pressure, is inflating the front tyre (of two otherwise identical tyres) less to give it more grip and thus better turn-in, or, if you prefer less understeer, while the harder rear tyre will slide more easily and thus add additional oversteer. That is, the bike had now been tuned away from its safest commuting or touring state towards a road competition state.
My next bike had the latest killer hub brakes front and rear; they left the best disc brakes for dead; I hated them because they were always trying to give me a faceplant, on or off, no nuance. In addition, there was nothing I could do to adjust their relative gripping strength, so that whatever retardation they decided upon was what was delivered to the contact patch of the two tyres. This bike also had computer-controlled adaptive suspension only in the front, which would soften the suspension at speed, and make it stiffer when the rider slowed down, so that the fork would go solid just when the brakes were reaching peak grip, resulting in a faceplant, or at the least an anti-social, embarrassing, dangerous uncontrolled stop. This bike was fitted, first with a workalike tyre that on inspection appeared to come out of the same mold in Indonesia as the Schwalbe Marathon Plus, so when those tyres got flat-spotted from too many spectacular slides, I fitted real Marathon Plus 37mm wide, which was a mistake. Those wretched tyres tried to kill my back. Eventually I under-inflated them, the front one to give some compression in the last stage of any hard stop, the rear one to get the roadholding at speed back to what it was (predictably consistent) before I started buggering around with what I could control -- the tyre pressures -- in order to correct the designer's errors, of which the worst, admittedly, was a saddle like a malicious wedgie (on a deluxe commuter!), which I threw off before I rode ten paces on it.
My next bike was designed from the ground up to ride on 60mm Big Apples, and I was in a position to specify the rest of it in detail, for instance the weakest (largest compression chamber) of the Magura rim hydraulics, which have been an absolutely brilliant choice for the particular bike and my riding style. Today I inflate front and rear the same, but perhaps lower than most cyclist who ride on similarly rough lanes would, but I tried various inflation regimes before returning to the first one I tried, very low and equally. The cost of all this comfort and security has been two snakebites in getting on for twenty years; I can't even say with any certainty what it has cost in extra tyre wear. My bike is expensive and a very big hassle to source and import, so I wasn't surprised when a lady wrote to me and asked if she could come from Dublin, a round trip over 300 miles, to ride it before attempting to order one like it. She loved everything about my bike but said it was a bit heavy on the steering at speed on a curvy downhill. I explained that I like it that way as a safety feature, and demonstrated that the steering could be made finger-light by just inflating the tyres higher. She frightened herself witless -- and me, following in her car, too -- when she came within inches of the thorny gorse hedge, definitely not a bike-friendly feature of the Irish landscape; I didn't fancy having to track down another in the colour scheme of British Racing Green with gold coastlines by a fellow who had been an apprentice on the assembly line in 1936 when the basic design was first made, and who in the year he lined my bike was officially declared the Master Craftsman of Europe by Volkswagen.
This was also the bike on which I made my first front drive electric motor experiment, with a motor which arrived already built into a narrow rim, which also came with a 35mm tyre by Vredestein (POS), so I tried it. This would have made a successful bike for a novice or a casual cyclist. Its main characteristic was safe understeer, which also meant it was less disturbed on bump by the uneven and sometimes even treacherous lanes of the West Cork countryside.
We've now arrived, via a set of examples of which I have experience, not just theoretical knowledge, at a point where I can answer your question. I too might have tried the fat front/narrow rear tyre distribution that you posit, had the occasion ever arisen, because I hate having road irregularities delivered via the frame straight into my hands and wrists as stress-frequencies. The problem is that I would have had to change riding style, and had to back off from the edge of adhesion to a riding style more suited to my age. Duh, dull.
Of course, if you normally ride with a sensible safety margin, you may never discover what is theoretically wrong with the fat front/narrow rear setup. If you do decide to try, start slower than you normally ride, and don't forget to let us know what you discover.
All of this is given on the assumption that we're talking about day rides. If we're talking about touring with any kind of a load, even just a saddle bag, never mind the loads we see the real transcontinental tourers on the forum carry, it seems to me obvious the fat tyre had better go on the back.
There's an additional point to consider: pedaling the fat tyre will be more efficient than the thin one, because the fat tyre's contact patch is not only larger but more optimally shaped.
Good luck.
