I've done them both on 700x28 Armadillos several times - no problems - but never with a load. I think you'd be okay if you went slow and were careful. They're roads that you could take a car on - not Jeep roads. I wouldn't hesitate to take my LHT over either of them. I'd just be careful not to slip in some gravel, and watch for big bumps so I wouldn't break a spoke.
If you go over Stagecoach Road you'll take Monterey Street to 101. It's only a mile or two from where Monterey goes onto the highway to the center of SLO. The north end of Monterey is hotels and restaurants. I think there's a Chevron station right before the highway. You could probably fill up on water there. The next water is in Santa Margarita, over the top of the grade. I think two water bottles each would be enough. That's all I've ever carried, but I've never carried a load. I might take three just to be sure, since I'd be a little slower and working a little harder. After that you'll be in and out of civilization - water will be no problem. If you turn off of El Camino Real to the right onto Highway 58 in Santa Margarita there's a nice city park about a block or two away - water, bathrooms, and picnic tables.
If you go over Santa Rita Road you'll be on dirt a little longer, but I still think two water bottles would be enough. (If you have a third water bottle cage and bring a third bottle you'll definitely have enough.) If you go that way the last place to fill up on water is in Morro Bay. There are gas stations, grocery stores, convenience stores, Taco Bell, etc. You can turn left on San Jacinto (towards the ocean) and there's a beach access park with bathrooms and water. When you get over the top of the mountain there's a winery tasting room on Vineyard right before you get to 101. I've gotten water there before.
If you decide to stay on pavement and go over Highway 46, the last place to get water may be in Cayucos. If so, I'd fill three water bottles. It will be a long way and a long climb before you get to Paso. There's a long (though gradual) hill out of Cayucos, and then the longer and steeper climb over 46. Before you get to the turn from Highway 1 onto 46 there's a little town called Harmony on the right. I think you can get water there, but I'm not sure. It would be nice if you could. If I were you and considering going that way, I might try emailing the slo bike club (
www.slobc.org) and asking if anyone knows if there's water at Harmony. It's a tiny town - the population is around 90 I think. The last time I was there there didn't seem to be much open. There were portapottis, and I think there was an artist's studio where the guy was working, but water? I don't know.
If you were to go that way, rely on getting water in Harmony, only to find out that they didn't have any and you were about to start over 46 without sufficient water, I'd keep going on highway 1 past the 46 turnoff. It's only a couple miles more to Cambria, and they have everything there (including CambriaBike). If you wanted to make a two-day journey to Paso, you might even consider riding a few miles past Cambria to San Simeon State Park. There's a hiker/biker site there, showers, and a nice ocean beach (and it's only a couple MORE miles to Hearst Castle.)
Let me know if you have any more questions.