star trek tng - Was Voyager really significantly slower than the Enterprise-D?

Simple answer: the writers messed up badly.
As far as I can tell, if the 'just over 300 years' line is accurate for the Enterprise D at Warp 9.2 to travel through 2.7 million light-years... that amounts to about 41.2 Ly's per 25 and a half hours (or just under 1 day in Trek universe - they have a 26 hour day then).

If we take this as an estimate of how fast Warp 9.2 actually is in the late 24th century (which DOES make sense btw), and if we take into account that per Trek itself, after warp 9, each point (or every 0.1 increase) would yield exponential increase in speed, and past Warp 9.9, the closer you get to TW threshold (Warp 10), again, exponential increases ensue with every (0.01) addition.
So, theoretically:

Warp 9.2 = 41.2 Ly's in just under a day.

Warp 9.3 = 82.4 Ly's in just under a day.

Warp 9.4 = 164.8 Ly's in just under a day.

Warp 9.5 = 329.6 Ly's -//-

Warp 9.6 = 659.2 Ly's -//-

Warp 9.7 = 1318.4 Ly's -//-

Warp 9.8 = 2636.8 Ly's -//-

Warp 9.9 = 5273.6 Ly's -//-

Warp 9.91 = 10547.2 Ly's -//-

Warp 9.92 = 21094.4 Ly's -//-

Warp 9.93 = 42188.8 Ly's -//-

Warp 9.94 = 84377.6 Ly's -//-

Warp 9.95 = 168755.2 Ly's -//-

Warp 9.96 = 337510.4 Ly's -//-

Warp 9.97 = 675020.8 Ly's -//-

Voyager's 'top cruising speed' was stated to be Warp 9.975
Top cruising speeds indicate a sustainable velocity an engine can take without refuelling or stops.
For Voyager, Warp 9.98 or 9.99 for example would be 'sustainable for only 12 hours'.

But hey, even if 9.975 was sustainable for only 12 hours... Voyager would traverse 75 000 Ly's in about 2 and a half hours at that speed.
And if that messup of 'Threshold' episode is taken into account, Voyager cannot even approach 9.975 before beginning to fall apart. Chakotay ordered a reduction to 9.5 0 which would still mean Voyager would need about 9 to 10 months to get back to Earth.

Mind, you, if Warp factors double past Warp 9.9 for each incremental increase (0.01), that would mean that Voyager at Warp 9.97 would cross through about 5273.6 Ly's in just under 1 day (probably closer to, or exceeding 6000 Ly's per day when you factor in the small 0.1 increases I didn't take into account).
So, Voyager would need about 14 and a half days to get back to Federation space with 5273.6 Ly's crossed each day... and about 12.5 days if its 6000 Ly's per day.

Voyager's writers placed its Warp 9.975 top cruising speed to equate the Warp scale of Kirk's era it would seem.
There is a solution to this particular issue:
It could have been explained that the Caretaker's pull into the DQ damaged the warp drive to such a degree where the crew had to 'redefine' the Warp scale themselves to the previous Warp scale until such a time came when they could repair the engines.
Each new year of the series could have began with the crew making series of repairs that increased their top sustainable Warp speed.
They could have done that so that the ship would return to Federation space under its own power in 7 years without external help or shortcuts of any kind.

Small note: Federation ships in the 24th century are equipped with plethora of tecnologies that would allow them to be completely self sufficient.
For instance: Voyager could have stopped in any un-inhabited star system, and used solar power to power its replicators.
Since replicators convert energy into matter, they could have easily replicated parts of industrial grade replicators and even antimatter (since they wouldn't be drawing from the ship itself), or they could have used this energy input to synthesize omicron particles which could have been used to boost antimatter reserves, and subsequently build more torpedoes.
Transporters could have been used to dematerialize large chunks of asteroids and re-arrange their molecular structure into what was needed.
Remember that all matter in the universe incorporates base materials, and asteroids are chock-full of raw matter. Just play about with the molecular bonds until you create what you need.
We already do it in real life and its actually automated, for the Feds in the 24th century, that kind of tinkering would be automated and perfected to such a degree that they would be way past that.

And seeing how Voyager could have been said to have been the ONLY ship in the fleet to sport these new engines (thanks to it being state of the art and all), there's your issue of them being unable to get support from the Federation any time soon.
That still leaves the problem of subspace communications being much faster... in which case, a message would get back home in about 14 months... but I guess a delay of that kind would have been acceptable for this series (wouldn't do them too much good because they couldn't expect SF to send any ships with retrofitted engines to their aid until after they initially got the message - so that would still leave the ship unsupported for at least the first year and a few months time).

Tons of ideas and missed opportunities could have been used.
Mind you, I do like Voyager, but I felt it was too dumbed down in various areas for a technologically advanced civilization that is supposedly way past us.
For the love of Humanity, even back in 1995 when Voyager first aired, we had the technological abilities that would put a shame to a lot of what Trek did by then.