The game does not explain the way that weapon range works very well at all (and the tooltip doesn't update, as has been a recent suggestion), so what you wrote is very reasonable on first glance, but its not the full picture.
The way range is calculated is that the "base range" is first multiplied by (1 + the sum of all bonuses) then by (the product of all maluses in form (1-malus)). Paragons have a base +100% hullmod, and gunnery implants gives +15%, so a 'full' range tach lance paragon (without advanced optics, which is tacked on afterwards I believe) is 1000*(1+1.00+.15) = 2150 range. With unstable injector it becomes 1000*(2.15)*(1-.15) = 1827.5 range.
High scatter amplifier operates on the base range and reduces all range past 200 by 50%, so 1000 becomes 600. (200 + (1000-200)*.5). So the 'full' range goes to 1290 and the range with unstable injector goes to 1096.5. So its roughly cutting the range in half compared to a 'normal' paragon. Attached is a picture of a paragon (just mission sim, so no gunnery implants) with an HVD and a Tach lance with HSA - the outermost yellow mark near the top of the shot is the range of the HVD. Without HSA, the tach lance would reach to just shy of that mark (because the weapon is set slightly farther back) as they both have 1000 base range.
Unfortunately, energy weapon mastery also works on the range in combat, not the base range of the weapon. So the enemy needs to be within 600, so about halfway in on the length of the beam, to get the full damage boost from it. This isn't explained well in game.
[Edit] Oh, you're playing on a version before the more recent HSA nerf! Ok thats not as bad. Its still not great IMO but its not as bad a range hit as now.
[Double edit] aaaand it seems you already knew all of what I was typing
Well, I guess I'll just remark that for a slow ship like the paragon range is very important.
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