The first thing I want to share is that my Engineer is a Gnome. So she starts her skill at 540, but she has to level up to 615 so it balances out. I double-checked myself with Wowhead along the way to make sure that my recipes looked comparable to their values at several parts of the process. I believe my experience should be the same as you non-Engineers, except that I can learn recipes a tad earlier than you can. That said, I tried not to use those recipes until the proper level.
When you pick up recipes from the trainer at 525, the first two are yellow. You also get a handful of other recipes, but you need to make parts before you can do anything else. As I'm sure you've come to expect, your first wave of crafting will be making bolts and gunpowder. These items both turn gray at 550. Since we'll be using a lot of them to reach the cap, you may as well go all out and do them now for skill points. If you like, you can also make a few Tinker's Gears while the recipes are still yellow. The G91 Landshark is another inexpensive option for this skill range.
Once you reach 550 you'll need to switch it up and start making Tinker's Kits. This is the cheapest item you can make in this skill range, it requires just 4 ghost iron bars and 2 windwool cloth. You're going to keep making these until you reach 580 skill, it took me about 30 of them to get there. The recipe turns yellow at 575 but you can still get good skill points from it.
At 575 all of the orange recipes in your list will require at least one Spirit of Harmony. So when you're sitting at 580, the next best option is the Thermal Anvil. The recipe is yellow at this point, but it's the only way to avoid massive SoH farming. Therefore, I'm proposing we use this yellow recipe for at least the next 15 skill points. This is the part where Engineering gets ugly. Each anvil requires 13 ghost iron bars (26 ore) to make. I had to make 25 of them to get 15 skill points. That translates to about 325 bars or 650 ore -- just to get 15 skill points.
At 595 the Thermal Anvil will turn green. I can't reasonably suggest that you continue using it, but the other options aren't much better. I think at this point you'll have to break down and farm at least one Spirit of Harmony. The two cheapest options here are Lord Blastington's Scope of Doom or the Mist-Piercing Goggles. The scope requires only 1 Spirit of Harmony, but you must also have 2 primordial rubies to make it. The goggles do not require mats from another profession, but they do require 2 Spirits of Harmony. So it's up to you which way to go.
Here's my progression list for leveling Engineering:
525-550: High-Explosive Gunpowder (need 135 for later)
537-550: Tinker's Gears (2 bars) or 5x G91 Landshark (4 bars > 2 sp)
550-580: Tinker's Kit x 30
580-595: Thermal Anvil (made 25 to get 15 skill points)
595-600: Mist-Piercing Goggles | Lord Blastington's Scope (requires JC)
I strongly recommend that if you're not in a rush, you should take your time and make the fun toys that are available while you level. Cranking out massive bolts/gunpowder/tinker kits/anvils is not fun and may not be a worthwhile use of materials. This list merely represents the cheapest way to cap Engineering, not the smartest way :)
Realm First Thoughts
I'm not going to characterize this as a tip because there are no tips here. The truth is that Engineering is ugly towards the end, even more so for the last 5 skill points. At 595 every recipe is green except for those that use Spirit of Harmony. I can't honestly recommend using a green recipe for skill points with mats as high as the anvil. On the other hand, farming motes of harmony is going to take a while too. Grinding out the last 5 points on the thermal anvil could be a bit faster if you get lucky with skill points. The main reason to go with mote farming is that the skill points are guaranteed for crafting those items.
The easiest item to make if you don't have a Jewelcrafting alt is the Mist-Piercing Goggles. This requires 2 SoH and 1 stack of ore for bolts. If you have JC who can prospect ore for you, I would opt for the Lord Blastington's Scope of Doom. You only have to farm one SoH, but you need 2 primordial rubies as well. To get 2 rubies will likely take 12-15 stacks of ore, which can be farmed in 45-60 minutes. You'll also need 2.5 stacks of ore for bolts. In my mote-farming test I killed about 200 mobs over 90 minutes time to get 10 motes of harmony. That works out to a drop rate of about 5%.
If you're doing the math here, the Mist-Piercing Goggles will take about 3 hours for the 2 SoH plus another 10 minutes or so for the ore to make bolts (unless you have 8 left over). The scope will take around 90 minutes of mote farming plus an hour of ore farming. These two are close enough in time investment that sluggish ore spawns could put the scope behind the goggles. Bear in mind that neither of these estimates include the time needed to reach 595, we're talking only the last 5 skill points.
I have to say this is the only profession I've hit so far where I hope I'm wrong and the skill tree gets tweaked before launch. To my mind it's somewhat sad that our least loved profession is getting smacked below the belt with an ugly grind.