Ok, there is really no reason to not run Wheel of Fortune. Its a good way to restock after you've burned your hand.
You have correctly Identified the need to run a slightly more robust Artifact Hate suit. And I like Hearth Kami. I also think that running a 3-4 mox monkies is a good idea.
-3 Chalice
-3 Goblin Cadet
+4 Hearth Kami
+1 Gorilla Shaman
+1 Wheel of Fortune
Magus of the Moon is one of the strongest cards that a Mono Red deck can run. What many don't realize is that Magus of the Moon does not change the -SuperType- of a card. So lands that are non-basic ~stay~ non-basics. So Running Magus and Price of Progress in the same deck is fine. In some cases its actually better because Magus prevents Wastelands and Fetches from being removed to dodge Price of Progress. So if your opponent has 2 Fetches and a wasteland that are All turned into mountains - they still take 6 from price of progress.
-4 Jackle Pup
+4 Magus of the Moon
The problem now is that your mana base needs to be tweeked to accomidate both the higher CC of Magus AND the fact that your still want to use Price for Progress as your finisher. So I would suggest the following:
-5 Strip/Wasteland
-2 Fetches
+4 Ancient Tomb
+3 Mountain (or Lotus)
Ancient Tomb is nice because it gives you the abilitiy to power down a turn 1 Null Rod OR with Simian Spirit Guide, a turn 1 Magus of the Moon. Pairing back the fetches will make sure you don't end up getting lands stuck under Magus that make Price unplayable.
Now we can think about Lava Dart. Lava Dart is another way to get those non-basic mountains out from under Magus. Asside from that Lava Dart is going to become a great substitute card for Mog Fanatic under the new rules. It can double up on Welder, Confidant, and other X/1 cards - while still retain its ability to ping players for final points and kill X/2's in a pinch. Most likely 3 darts will be enough to handle whatever comes your way.
Finally, we can look back on the deck and see we've removed a good amount of 2/1 meat. The deck could definately use another finisher card. I'm a big fan of 'burn' style decks running either Shrapnel Blast or Firey Conclusion. These cards can be very powerful and unexpected. You don't really have the artifact count to make good on Shrapnel, but you do run some 'bulk' creatures. Extra Lavamancers, extra gorrilla shamans, even a 2nd Magus now all become game-ending flings.
You can also run something a little more meta-gamey: Fireblast is a catch all that works well with the Magus/PoP combo but can sometimes compete with Lava Dart. Mog Salvage is a GREAT card if you face alot of Tezz or other blue-Timevault decks. Pulverize can be used as an answer to Inkwell. Lastly Fork can be a decent card as well. Fork be used as a counter-counterspell, as well as something to double-Price someone to death. I don't think you really have enough good instants and sorcies to use fork though.
-1 Lavamancer
-4 Mog Fanatic
+3 Lava Dart
+2 Firey Conclusion / Fireblast / Mog Salvage / Pulverize
The changes you are proposing are not changes, is another deck. Yes, both are red, but hear ends the similarity.
The deck that you mention is similar to Stax. A low aggro with bombs, but the deck I post is near Fish. An Agro control with small but fast pets.
Shuster, figure of destiny could be part of the deck, but they need a lot of mana, and seems slow. But cards as magus of the moon and whell of fortune are moreover slow.
The game plan of this deck is chalice+REb (if needed) or Mountain+SSG+Null rod or Gorilla shaman, or 2/1+ 2/1 reb, to fight against Tinker and tezzenet. The cc1 2/1 give the speed that other creatures (as sage of epytir, cursecatcher, Spellstutter Sprite or magus of the moon) havent got. We must disrupt out opponent mana base, fighting lands and artifacts, and retarding/dificulting combo, but killing quickly, not giving oportunity to our opponent to search the card he needed.
An earlier pair of 2/1 plus one 1/1 or bolt could kill before inked leviantan attacks for three times.
Null rods, kamis and Smash to Smithereens are so good against vault. Mox Monkey can kill the voltaic key and Lightning bolt can end with tezzenet
Our creatures jump the Remora and usually meditate canīt be played.
Fighting against Stax weīve got a lot of permanents, a good mana base with simians and basics, and good removal.
Against Fish, lavamancers are awesome, as well as bolts. Fanatic still being good. REbs are a very good counter and swords against ninjas snd others. Against BUG Fish, relics in the sideboard and PoP gives us a good chance.
Against tendrils we need an early chalice or Pyrostatic, but is a hard match up, idem that ichorid, but we have, fanatic, lavamancer to lavamancer or another creature, bolts to our creatures, kami+target... and a good sideboard.
A normal hand will be:
One Null Rod/chalice/Shaman/Wasteland---}Disruption
One fanatic/lavamancer/Shaman/kami---}Agro/Disruption
One fanatic/lavamancer/Pup/kami---}Agro
One Pyrostatic/REB/kami/Smash to Smithereens/Wasteland---}Disruption
Two Mountains/Mountain+Simian/Mountain Wasteland---}Mana
One Bolt/Other---}Depending.
As we can see is usual to have a hand with decent disruption and decent first turns Agro. A good equilibrium in these concepts is the reason of this deck.
I can remember the "TinkerExtended metagame" with Stax, Twidle Desire and other powerfull decks, but, surfing the metagame was RDWs, with cards like tangle wire, pillage, pups, firebolts... it was another time, another format, but the esence is the same: Fast creatures + Fast disruption=Good tempo.
I know Fish disruption is better, thanks to FoW, Daze and Stifle, but well focused, and we are faster, for this reason we need less powerfull disruption,
If I can kill one turn before I need one Fow less.