If you are carrying a lot of fluid that would probably explain your larger fundal height also don't forget.
I had a growth scan at 34+4 and they told me my baby was/is huge. A biff! Outside of the top 95 centile, so in the top 5 centile based on some of the measurements.
According to the scan babys head was measuring at 36+5 and tummy was measuring at 38+5

And Registrar told me that baby was about 7lb/3kg based on these results. I was carrying 'normal' fluid levels and baby movement was recorded as good.
FWIW, I think they are a fair bit off. Sonographer had alreay said the head result was not accurate as baby had head way down so hard to get a decent reading. Tummy was large but still awkward to get a good reading.
Then when I saw my MW at 36 weeks she measured me and I was only measuring 37cms fundal height, which is only one week ahead. I've been one week ahead since around 30 weeks. She says I don't have a massive bump, that its neat and if fluid levels are normal she can't see how I am carrying a massive baby in there. Large maybe, but not scarily so. She had a good feel and prod of baby and says she thinks baby is not fat but long. Said babys spine felt very long down my tummy and she feels I'm not carrying a huge fat normal length baby but a longer one with a bit of chubbiness

And being long would explain why so scrunched up and hard to scan. I have a long torso so can apparently cope better with a longer baby than most. She felt if I had a huge baby I'd be suffering a lot more with heartburn etc and would be in discomfort higher up as baby would take up so much more room. As it is LO has plenty of space to turn side to side while remaining head down.
I get another growth scan at 39 weeks but tbh, I won't read much into that then either.
I think my MW is closer to the truth than the Doctor. I am 5'9 and large framed also. A slightly larger head does worry me a bit, but as my MW said, if its too large baby simply won't descend to be born. If baby starts to come down then s/he will appear just fine. I am however doing daily perineal massage to help with this part just in case. Frame wise baby would hopefully have stopped growing then, it will be fat being laid down, not head size expanding massively.
TBH be it 8lb or 10lb, baby will hopefully be born naturally. My MW tells me she has seen women who are small, 5'4 or so deliver 8-9lb babies and one lady delivered 10lb plus. My MW said that if I was broad shouldered but narrow hipped she might be a bit more concerned but as I am both broad in the shoulders and have wide hips she reckons our LO will find a way out well enough
The Registrar I saw talked hospital birth due to size and mentioned induction once overdue but again, I declined either and remained with my homebirth preference. More chance baby will arrive just fine if I remain out of hospital and away from those sort of procedures from what I have read and found out.
I think you have to wait and see how things go and make your decision based on an informed choice. Do some reading on birthing larger babies, its far from doom and gloom and many women birth naturally just fine without being induced etc. TBH an induction is forcing your baby to be born when its not really ready, so who knows how that will go. You will be limited to what you can do then also, so maybe wont' be able to use movement and gravity as you would otherwise. You really need to research all your options.
Fair enough if overdue by a bit or there are medical concerns, induction/C section might be best for you, but if baby and you are well, please consider all your options and don't feel you have to do as they are suggesting. If you are informed of all the facts and both sides of the coin, you can make the right decision for you.
I'm just a great believer in being informed and having options, not just feeling there is only one way for things to happen because someone, even if that someone is a Doctor, says so. Not being informed I feel is more scary than knowing the facts and being able to choose what feels right for you based on those.
Erm sorry this was so long winded

Hopefully its been of some use.