I Don't even consider it an hgv, the design imo doesn't have enough L/D ratio to be considered an hgv, or a gliding body, it looks more similar to an AAM missile, or US SM-6 missile, looks like an enlarged SM-6 missile .
And while it does have a booster that takes it to much higher altitude for it to then dive down till it's cruising altitude, it doesn't leave the atmosphere unlike hgv boosters, and doesn't seems to be using altitude as it's primary means of gaining speed and range, more like altitude is a "supplementary" element rather than primary/main element unlike HGVs.
It's a unique system/missile.
Its a missile that can do mach 8+ sustained cruise at lower altitude(30-50km) with the help of its rocket motor and still remains hypersonic( mach 6+) even in terminal, with this alone, it's more difficult to intercept compared to even what we currently know about scramjet powered hypersonic cruise missiles that are in development.
And while if drdo had used a hgvbody/more lift generating body for second stage, more range could have been gained, but sacrifice in control and maneuverability will be needed to be made, in its current design, the second stage/KKV of LRASHM has relatively very high controllablity and maneuverability compared to HGVs, conical RVs, and even scramjet cruise missiles( air breathing engines need stable air flow so high angle maneuvers are not good for that), which is good when you wanna hit moving targets like ships, and make interception more difficult.
In LRASHM, Drdo sacrificed, range & lift, for controllablity, maneuverability, lower flight profile, and difficulty of interception, mainly because I think 1500+km range was deemed sufficient, and lrashm in its current form does provide this range.