BardStephenFox, it takes as much work as you are willing to put into it. There is no problem with adding any existing DMG item into a campaign that utilizes the rules from this book. The power of this book comes into play when you or your players make new magic items.
While Artificer's has a completely new set of feats to do that, the feats in the PHB are perfectly compatible. So, for those of you that think it makes no sense to have two different feats to create a ring of flying and boots of flying, then this book has what you want. Otherwise, the existing item creation feats work as advertised in the PHB. No change there.
The biggest change comes in how you calculate the cost of the magic item being created. No more guesswork (well, items like Crothian's aside!). It's also designed to give characters with higher intelligence/charisma/wisdom more item creation power. So, a wizard with a 24 intelligence can create more items than the same level wizard with a 16 intelligence. It doesn't work like that in the core rules.
Or, use the core rules exactly as written, and use our rules to calculate the costs, ignoring the spell slot requirements. Or, just take advantage of the variant rules like gestalt sets (a set of items that create new effects for each piece in the set), or socketed items. It also has instability rules, new item effects, a list of magic item components to add some realism to magic item creation, a random magic item history generator, and even a table for determining potion flavors. All of that works with the existing system.
Now, for your items:
Dreamstone
1 use-per month, "command-word" activated (this allows non-spellcasters to use it).
4 slots for use-per command-word activated, +2 for 1 use per month. 6 spell slots total.
Spell level 5, caster level 9 (no benefits gained from a higher caster level). Plug in our formula:
10gp(5 + 9 - 1) * 6^2 = 10gp(13)*36 = 4,680; market cost = 9,360gp.
Second item is a lot more complex. I'm not going to work up the base item "+3 longsword". That's a standard +3 bonus item, and has a cost of 11,000gp (weapons are 2x the regular cost because of having a bonus to to-hit and to damage).
To this we add 3 effects:
resist energy - fire, cold, and lightning. Now, the 3.5 version of this spell is 10 points and lasts 10 minutes. This item would actually be much cheaper with the 3.0 rules, because 3.0 has "endure elements" which is probably what this spell was based on. Endure elements in 3.0 has a duration of 24 hours, which makes making that spell permanent fairly cheap. It's cheaper to make a long duration spell permanent than it is to make one that is "instantaneous" permanent. For simplicity's sake, let's use the 3.0 rules for this item:
Endure elements fire, cold, lightning.
This is a continuous property, and will require the continuous item rules. Adding an extra effect to an item incurs a +1 cumulative spell slot cost to the item. The cost for a 1 day duration "continuous" item is 9 spell slots. So, these would +10, +11, and +12 spell slots since the swords +3 bonus is the first effect. Those are spell level 1, caster level 1.
10gp(1 + 1 - 1) *10^2 = 1,000gp
10gp(1 + 1 - 1) * 11^2 = 1,210gp
10gp(1 + 1 - 1) * 12^2 = 1,440gp
The last effect is a use-per "true reincarnation". Now, I'm going to take this that you mean "true resurrection" as the former doesn't exist. I'm not sure why "true resurrection" is needed here, as the body still exists, so "resurrection would suffice". But, hey, it's your item.
First, we add a +4 for the fourth effect.
Use-activated, 1 use-per year is 6 spell slots. (5 for use-activated, +1 for 1 use-per year). 6 +4 = 10 spell slots
Spell level is 9, caster level is 17 (feel free to substitute a different spell level and/or caster level if I'm mistaken on which spell you intend here).
10gp(9 + 17 - 1) * 10^2 = 250gp * 100 = 25,000gp.
This item suffers the same problem that Crothian's did. It requires 10 9th level spell slots for this last effect. There are two ways around this. As a fluke, if we calculate this effect *before* the endure elements effects, we can cost it with a +1 (instead of a +4) if we make this the second effect in the item, versus the fourth. It becomes cheaper, and more do-able. The second would be to create the item and be done with it, and then *add* the resurrection as an extra effect later, but let's just swap the ordering of the effects.
10gp(9 + 17 - 1) * 7^2 = 12,250gp (half as much, in this case). The endure elements become slightly more expensive as a result.
10gp(1 + 1 - 1) * 11^2 = 1,210gp
10gp(1 + 1 - 1) * 12^2 = 1,440gp
10gp(1 + 1 - 1) * 13^2 = 1,690gp
Now, you mention a drawback - the creature has to have a head. We'll assign that a -1 to the cost because of that limitation. There's a section on limitations that can be imposed on items to decrease the cost. That leaves us with 6 spell slots for that effect.
10gp(9 + 17 - 1) * 6^2 = 9,000gp.
Total cost 11,000gp + 1,210gp + 1,440gp + 1,690gp + 9,000gp = 24,340gp (creation cost); 48,680 market cost.