EO line 3+ miles from exchange

Hello
We live in an EO house in a rural position over 3 miles from the exchange (Cornwall). We have no 3G coverage and virtually no 4G. We get less than 2Mb download currently.
Fibre was installed underground through local council owned parkland (grade 1 listed!) to a converted fort that is about half a mile away (c100 flats). There is a new green cabinet there. There is an unclassified road from our property to the green cabinet near to the fort. There is also a grey underground "junction box" about a third of a mile from our property in the parkland.
When we were without any phone line for 6 months due to overhead cable damage (part of our line comes along electricity poles and we are the only property on the line), I had several chats with Openreach engineers ( who were always extremely helpful). One suggested that it should be possible to "hook in to" the fibre at the underground junction box. Is this correct?
The reason I ask is that I have the capability of digging the trenches required to get the fibre to my property from the grey junction box which would presumably keep the cost low(er)? Before I get in touch with Cornwall Development Company (the operator tasked with getting rural properties fibre), is this a solution?. I'm happy to stump up some money (and there appears to be local grants available to assist) to solve this, especially if it gives me FTTP.
I'm no engineer so have no idea if my presumptions about the grey junction box are correct in that it could be used for FTTP.
Would someone just confirm that, even if a new cabinet is put next to the exchange (which I believe is the solution proposed to get fibre to more properties that are EO), then this will not help me as we are so far from the exchange?
As we are the only house here, I think I need to be proactive in trying to solve the problem, particularly if there is a grant available to help soften the financial blow.
Many thanks
Rose

So the fort flats have VDSL2 by the sounds of it, so while some fibres pass by, there is probably not the splitter elements for a FTTP deployment, i.e. this will be closer to a built up area since the main node will serve around 1,400 premises and then sub divide until you get to a single manifold with 50 to 100m of the final 8 to 12 premises.

So you might be able to link into the fibre if there is a joint available.

Cost wise the fact its not been done yet via the project suggests a cost well above £1700 for the work.

Hard to say without knowing what's down the hole. If it's just a joint box then not going to help you . If it's a aggregation node ( unlikely) then your laughing

I would get in touch with the Cornwall Development Company and see what they have to say. The cost will depend on what is already present. Laying a fibre cable would be easier if direct burial is allowed.

thanks all for your help.
just to confirm on my last question before I talk to CDC (so that they don't fob me off as we show as EO Pending) - if Openreach install a cabinet next to the exchange, my service would not improve as I am so far from the exchange (over 3 miles)?
thanks
Rose

That's right

Yep, anything over (roughly) 2k from the cab and VDSL isn�t of any use.