Interesting, I have not been turned down (twice) by AAA drivers with my altered rig (in sig line). Simply told them what it was and a flatbed arrived. Maybe some are just lazy pricks? Are you a AAA driver? If so, what would your beef be with a blazer like the op is buying? Policy? Just curious...
I have to defend myself, only cause I've never been turned down either. Maybe this is policy, dunno, just saying from experience. I've had a 2007 3500 longbed Duramax Crewcab 4x4 lifted 6" with 35" tires....towed 3 times. Also a stock '97 dually crewcab. Both trucks need the larger flatbed. I've had to wait cause they either send small trucks or small flatbeds, but never turned down.

But I will call AAA now to confirm I'm covered. I increased my towing to 100 miles once I got the blazer.
Ok guys I will try to answer your questions as best as I can. Yes I am a 3A driver. First off your not always gonna get turned down. Some 3A contractors will haul anything. Reason being for the most part is they don't want to lose the money. Another reason is some wont turn you down is because all they use is flatbeds (due to the fact most drivers can only operate a flatbed) so they figure what the hell haul it anyways. I will admit that a lot of 3A drivers are focking clueless and don't care, nor do they know what they are doing. Heaven forbid they actually had to use a real tow truck.
Ok so here is what my beef would be with the OP's Blazer if I were called out to tow such vehicle. First off he would not get a flatbed. Reason being is because flatbeds are medium duty trucks. 3A only pays the contractors light duty rates. Let me put it this way, our light duty trucks go for $170 an hr and our medium duty's go for $230 an hr. Therefor we wont run a flatbed big enough to haul a K5 and not get paid for what the truck is worth. Simple as that, it boils down to profit. Yes we have light duty flatbeds, but putting a K5 on them puts them over weight at the scales. They are intended for the smaller AWD cars.
The proper way to tow a K5 is with a conventional sling truck from the rear. So if I show up in my conventional and the K5 is sitting on a 4" lift and say 33-35" tires it is to tall for my equipment. I would simply tell him that he would not be getting towed under 3A Tow trucks were designed for stock height vehicles it's as simple as that, and yes it is 3A's policy.
Now onto Octanes two trucks. I would not tow either of them under 3A. Both are 1 tons and 3A does not cover for 1 tons or larger vehicles, not to mention the lift on the D-Max. Again they cover us to run light duty trucks and there are weight restrictions. Myself I would tow both of your trucks, but you would be paying for it yourself out of pocket. I would also use a medium duty sling truck and tow both of them from the rear. Oh and trust me it can be done safely with out any damage. Just have to know the tricks of the trade.
People think because they have a 3A card that some how they are magically covered for any situation. There are so many rules and regulations it's not funny. For instance..... If you are on a dirt road that is not county maintained year round then you are not covered by 3A. We charge the commercial rate from the time we leave the pavement to the time we get back to it. Do people get pissed off, hell yes they do. Bottom line is we don't work for free though. Another one is if your vehicle does not have current registration or a moving permit then it's not getting towed. Want the old beater out back towed to the local wrecking yard? Sorry your SOL, they don't cover that. Have more than 2 people in the car? Well to bad sounds like someone is doing some walking or calling for a ride. Like to have old Rover sit on your lap? To bad his ass can ride in the towed vehicle, unless he is a service dog, and his ass had better be small and for a real good reason.
I could go on and on about this guy's, but I think you get the point. I have people argue with me on a daily basis as well as 3A's own dispatchers about the policy's and I have never lost an argument. Myself and the company I work for follow the rules. Problem is most Members are unaware of the rules. Oh and one last thing. People who think that I am there to take their frustrations out on are sadly mistaken. I will leave their ass on the road side and not think twice about it. They can file a compliant all they want.