Some stoves just work better than others for large boils. There are lots of posts where some have the problem you're experiencing and others say they get a full rolling boil with 4-5 gallons in the pot.
I can do 7 gallon full (AG) boils on my (Samsung) glass top stove, but have to keep the lid on part way or part time to keep it rolling. I know my stove cycles the power off and back on preventing it from continuously outputting at max capacity. It maybe a safety issue, or just a conservative approach.
Also, the enameled graniteware pot has an uneven bottom, concentric ridges and valleys, so it doesn't give you optimal contact and heat transfer from the glass top to the pot. The glass top has temp sensors and temporarily shuts off the element or reduces power when it reaches a certain temp.
You could split the boil, using 2 pots, 2 burners at the same time. One boiling 2.5-3 gals the other 1-1.5 gallons. Check to see what the second (usually smaller) burner can boil. You could put some Reflectix (2 wraps) around your pot to reduce heat loss through the sides. Just be careful the plastic doesn't get too close to the bottom and melt to your stove. SWMBO will be unhappy with that. I'd keep it at least 1/2" above the stove.
As said before, put the lid on, but only partially (like half way or 2/3rd way so some steam can escape and take some DMS precursors with it. Although DMS is less of a concern with extract brewing.
Spread your boil additions (brewing salts, hops, spices, irish moss) proportionally over the 2 pots. Then combine at the end of the boil and add your LME or DME.
+1^ on adding the LME at the end. It really doesn't need to be boiled or has much benefit from it. Even all DME can be added toward the end, or at least should be split, like 1/3 at the beginning and the balance at flameout.
I'm not sure exactly why, but I've read you need to add at least some LME or DME at the beginning of the boil. But for risk of burning, scorching, or over-caramelization, never the whole amount. 1/3-1/2 is common, but you may be able to do even less.
Partial boils with steeping grains or partial mashes can create wonderful beers. There are some limits on how hoppy/bitter you can get it since you'll be diluting at the end, but unless you brew 100+ IBU beers that's not much of an issue.