In the situation you describe, R1 is out on the force play.
Once he is out, we don't need any more information or additional events to make him "really, most sincerely" out. He's out on the force, and he stays out.
Now we have to decide if the slide was legal and if there was interference.
As you quoted earlier, the relevant portion of the definition of an illegal slide says a slide is illegal if "the runner goes beyond the base and then makes contact with or alters the play of the fielder."
In your scenario, in which the contact occurs at or near the front edge of the bag, at or before the time one or both legs extend beyond the bag, it doesn't sound like he went beyond the base "and then" made contact.
Maybe if you described the contact--what part of the runner came into what part of the fielder with what effect--I could understand how he could get one or both legs beyond the back "and then" make contact at the front of bag. But I don't see it.
I don't need extra words in the rule book describing the location of the contact to decide this is slide is legal. The only way he could get one or both legs beyond the base "and then" make contact at the front of the base would be if he did something else illegal, like a pop-up slide.
Absent additional information, I have a legal slide in this situation. He has a leg and a buttock on the ground, he didn't raise the upper leg, he didn't slash or kick, he didn't try to injure the fielder.
If the principal reason the double play was disrupted was the infielder's failure to get out of the way of a legal slide, all I have is a force out and a live ball.
There is a case in the 2014 book that says, "With R1 at first base, a ground ball is hit to F6, who throws to F4 covering second. R1 slides late at second, stays in the baseline, but R1 makes contact with F4 who is in front of the base, causing him to overthrow first base." The ruling is "Providing the slide is legal and the contact is not malicious, there is no violation."
The only variation your scenario adds is one or both feet eventually going beyond the bag. I don't think it changes anything in the situation you described.