[alexander_busek]

I thought that is what commas are for, to place the modifier on one side or the other.

Okay, then let's see you insert commas into the two example sentences so as to produce each alternate meaning:

Studies show that reading often improves memory.

The house that got a new roof recently was sold.

Looking forward to seeing what you make of those two sentences!

I, personally, would rather re-arrange the word order to obtain the desired clarity.

Regards,

[PhiloBedo]

Studies show that reading, often improves memory.
The house that got a new roof, recently was sold.

Studies show that reading often, improves memory.
The house that got a new roof recently, was sold.