Are there sites other than LNER which sell their 70min flex tickets?
The DfT are keen to abolish (Super) Off Peak tickets, so other companies are introducing "Flex" type tickets, with a loss of refund rights and/or flexibility, but LNER are the only company specifically doing 70 min flex.
eg can the Forum's site sell them if the correct buttons are pressed?
Yes, for example if you want an expensive train, such as the 0701 Newcastle to London...

...you can choose any train +/- 70 mins that is significantly cheaper...

...then click "change ticket selection" and choose 70 min flex and, if available, purchase that instead:

(Screenshots above show the 0701 NCL-KG priced at £175.80; the 0758 at £110.19 and a 70-min flex for the 0758, which is valid on the 0701, for £157.90)
In order to be "simple", customers need to search for trains they don't want, to see if the Flex fare is cheaper than the less flexible fare for the train they actually want. This is currently a trial but is being deemed a success by the DfT and they want to roll it out across the country.
What we'd like to do with the forum site is to "pre-flex" the tickets, so that if you choose the 0701, we would automatically offer a 70 min flex ticket for the 0758, but I am not sure if the train companies will allow this, so it may not happen.
For now, you need to check the prices of all trains in a 140 min time window, to get the best price (this is considered more simple than buying a Super Off Peak ticket).
My travel, usually from London to places like Wakefield or Newcastle is somewhat unpredictable as to exact time, but needs to be as quick as possible once confirmed. I'd like to take advantage of Advance prices, say from 1 week ahead, but have price guaranteed and a modest amount of flexibility
The flex tickets may not be cheaper than on the day Advances, especially if splits are available; it's a way of locking people in and making them commit to paying a ticket which may not suit their needs. This is the very definition of "success" according to the DfT.
But yes, you can do this using the forum's site, and it will work with other operators when it's rolled out.
Some operators are being directed to replace their Off Peak tickets with semi flex tickets that allow travel all day rather than in 70 min timebands, the main differences being they are non-refundable, subject to surge pricing and may be quota controlled.