I agree. Having the four base ambers at the start would really make everything feel rushed. I think, from a TV series point of view (Yes, I know what we're doing is only a fan project, but using a TV series format helps with the organization), that for the sake of having constant things to look forward, the forms could be organized the following way:
Thero Class-"Episode" 1-Base form
Quadro Class-"Episode" 6-Tank form
Aerial Class-"Episode" 9-Agile form
Aqua Class- "Episode" 17-Gunner form/Upgrade to counter the Secondary Rider
Omni Class-"Episode" 23-Super form
Extinction Class-"Episode" 32-Final form

Exactly what I was thinking.

I'm fine with him getting the amber later on, but let's make the situation like this: He first receives the Paleo gear with the thero amber by the museum. A little later, they create his quad amber. Then they create his aero amber, then aqua, then omni, and the extinction amber by attempting to create the perfect counter for The Extinct.

I dunno. the idea of the museum making the form which ultimately is making him a monster kinda makes the museum seem either evil or irresponsible.
I dunno. it could just be me.

Why not make that the point? This final form is all about questioning the boundaries between good and evil to begin with.

because WHY would they make a thing that's supposed to fight extinct make ANOTHER Extinct?

For SCIENCE! Or maybe because there's some corruption within the staff. Perhaps somebody made a deal with the Extinct. Or maybe some other reason entirely. There's plenty of potential explanations.

We've already decided on a museum making his rider gear. The museum is where Ray's parents work. The museum has good intentions, even when creating the extinction amber because they try to take away the corruption in the Extinct DNA for Paleo to have a counter for the Extinct, but when he tries it, it gets corrupted again and his final form becomes unstable.

What if the extinction stone already existed early in the story? We could make it that the museum made it out of the DNA of the extinct he defeat as the story went on , continuing to experiment witj it. but upon testing it, they found the stone to be unstable and deadly that they refrained from giving it to Ray until it becomes safe for use. or until the situation called for it.

We could also make Omni form one of their attempts at making a safer version of extinction form but due to not having enough extinct DNA in it, it wasn't as strong

we could have it to where some of his amber stones get destroyed, so he HAS to use it.
I think that would make more sense than having him use it with the museum's consent and then backfiring.