Future Design: AS-SO3-E "Overreach"
The "Overreach" shell uses our extensive knowledge in the manipulation of circuits, magegems, and fireballs to create a devastating shell.
Inside the Overreach are two AA-size Magegems, connected in series by crystal wiring. These Magegems are purposely overcharged during creation, creating a notably unstable effect. But without introducing any more magical energy, the Magegems will remain stable. Another AAA-size Magegem lies within the shell. A pressure-sensitive circuit in the shell connects the AAA Magegem to the AA series. Once this circuit is tripped by the shell impacting ground or some other object, it'll detonate the shell via allowing the energy from the AAA magegem to be transferred to the AA Magegems, pushing them past critical levels.
Circuits placed on the AA Magegems are made to "tune" the detonating Magegems into a fireball form, making it appear as if the shells explode with the forces of several PSFs. Normally, each AA-size Magegem is enough for roughly one flare (and therefore roughly one PSF), but a lot of the energy used in summoning PSFs and Flares goes to making a stable projectile and giving it heavy momentum. Whereas the Overreach's detonation can forego those spell aspects in favor of a bigger explosion.
The Overreach is built with a crystal "tip", with the rest of the shell being made from metals. The crystal tip gives it mild armor piercing capabilities. The Overreach can pierce armor to a degree noticeably higher than our current standard shells, but not anywhere near the point where we could call it an armor-piercing shell.
The result is an awe-inspiring new weapon. A shell which explodes with the force of multiple fireballs upon impact, giving it a massive and devastating area of effect. Its mild AP capabilities allow it to be more effective against armor, too, piercing a small amount of it before exploding.
Since we're building most of the shell casing from metal, we can take advantage of our plentiful mountain metals to create this design. Our extensive knowledge with designing shells (such as the Equalizer), Circuits (Many designs), and Magegems, should make this design an easy task for us.
TL;DR: An explosive shell that detonates with the force of multiple fireballs using 2x AA Magegems. A basic crystal tip makes it a precursor to proper armor-piercing shells as well as giving it very mild AP capabilities. The explosion force is possible because we're using the energy just for the explosion part of a fireball, not the momentum or stable projectile aspects.
EDIT:
Also of relevance is the revision next round. I'm thinking upgrading Magegems, the steam engine, crystal upgrading, or crystal equipment.
Future Revision: Crystal Equipment
Our plate mail is cool and all, but it's not crystal. This is a problem! One which is easily fixed. With some additions to the Crystalworks, we can shift our plate mail production from metal to crystal and greatly improve our soldiers' survivability with harder and lighter armor.
Our broadswords have some application where our crystal axes don't. Let's make them out of crystal for harder and sharper swords!
Our arrows could probably be better. Let's replace the tips with sharper and harder crystal. Even if they make themselves a ripoff of our platemail but with their """"metal"""", they won't be safe!
Our soldiers have wooden shields. Let's remedy this with light and hard crystal.
Hell, if there's anything else that we can make out of crystal, let's do it.
Upgrading the steam engine is just self explanatory miniaturization. Upgrading magegems is self-explanatory. Upgrading Crystal (Polymer Crystal) was already posted earlier.
But what about the Crystal Spyglass? The problem with it is that it seems like something in between a Design and Revision. Too simple for a design, but too complicated for a revision. But it is potentially really useful, so...
Future Revision: Crystal Spyglass
Our Mathemagicians believe they have found a way that can change the optical properties of crystal. With some certain tweaks to the formulas in a Crystalworks production line, we can create a type of crystal that when properly applied, can actually magnify far-away distances and sites. This has immense application for our artillery, and the crystal has been quickly put in metal "cylinders" for use by far-away artillery spotters. Our artillery can find targets much more quickly, more efficiently, and more safely.
I'm not confident that we could get away with this in a revision, but I personally think if we make it a design, it should have some extra features making it worthy of a design. An enchantment highlighting enemies or living things? Something like that.