You can see all of your current missile techs listed on the missile design screen.
Your current tech should be from what you've described.
Warhead 3/msp
Agility 32/msp
Fuel Eff 0.7
Power multi x1.5 (converts to x3.0 for missile engines)
I'd really research another 1-2 levels in warhead and possibly agility before really making missiles. You can get away with the relatively low power multiplier due to running plasma engines now but should probably get that up soon as well.
I'll have a fiddle and see what missile design I can create with your current tech.
Edit:
Original missile
Missile Size: 10 MSP (0.5 HS) Warhead: 9 Armour: 1 Manoeuvre Rating: 12
Speed: 12000 km/s Engine Endurance: 110 minutes Range: 79.5m km
Cost Per Missile: 4.448
Chance to Hit: 1k km/s 144% 3k km/s 48% 5k km/s 28.8% 10k km/s 14.4%
Materials Required: 2.5x Tritanium 1.948x Gallicite Fuel x750
Using ion engines and sticking to your size 10 missiles. 3 spaces warhead, 0.5 fuel, 1.1 agility, 2 size 2.7 x3.00 ion engines.
Missile Size: 10 MSP (0.5 HS) Warhead: 9 Armour: 0 Manoeuvre Rating: 14
Speed: 19400 km/s Engine Endurance: 93 minutes Range: 108.1m km
Cost Per Missile: 5.384
Chance to Hit: 1k km/s 271.6% 3k km/s 84% 5k km/s 54.3% 10k km/s 27.2%
Materials Required: 2.25x Tritanium 3.134x Gallicite Fuel x1250
62% higher speed, 36% longer range, 89% better chance to hit by comparison.
Do note however that they use 66% more fuel which could be a problem if you are really starved for fuel. Also 60% more Gallicite if you are starved for that for some reason.
A size 6 variant using warhead 3, fuel 0.2, agility 0.3, 1 size 2.5 x3.00 ion engine.
Missile Size: 6 MSP (0.3 HS) Warhead: 9 Armour: 0 Manoeuvre Rating: 12
Speed: 15000 km/s Engine Endurance: 76 minutes Range: 68.5m km
Cost Per Missile: 3.567
Chance to Hit: 1k km/s 180% 3k km/s 60% 5k km/s 36% 10k km/s 18%
Materials Required: 2.25x Tritanium 1.317x Gallicite Fuel x500
25% higher speed, 14% lower range, 25% better chance to hit by comparison.
Smaller launcher means faster reload and more launchers in the same tonnage.
Moving on to using your newer plasma engines
Size 10, 3 warhead, 0.5 fuel, 1.1 agility, 2 size 2.7 x3.00 plasma engines.
Missile Size: 10 MSP (0.5 HS) Warhead: 9 Armour: 0 Manoeuvre Rating: 14
Speed: 25900 km/s Engine Endurance: 70 minutes Range: 108.2m km
Cost Per Missile: 6.194
Chance to Hit: 1k km/s 362.6% 3k km/s 112% 5k km/s 72.5% 10k km/s 36.3%
Materials Required: 2.25x Tritanium 3.944x Gallicite Fuel x1250
34% increase in speed and accuracy over the ion engined missile, as expected from simply switching to a higher engine tech.
Similarly for the size 6 missile. warhead 3, fuel 0.2, agility 0.3, 1 size 2.5 x3.00 plasma engine.
Missile Size: 6 MSP (0.3 HS) Warhead: 9 Armour: 0 Manoeuvre Rating: 12
Speed: 20000 km/s Engine Endurance: 57 minutes Range: 68.5m km
Cost Per Missile: 3.942
Chance to Hit: 1k km/s 240% 3k km/s 72% 5k km/s 48% 10k km/s 24%
Materials Required: 2.25x Tritanium 1.692x Gallicite Fuel x500
Looking at the difference in speed from what you posted, are you not increasing the multiplier on the missile engines when you design them? Or are you sure you actually used ion engine tech for them and not one of the lower engine techs?