Let's try another way to see if this makes sense for you. All the relevant rules have been quoted and the FAQ makes it clear that you cannot have ASF or ASL multiple times. So here are the situations:
1) Your model has neither ASF nor ASL. It will strike at Initiative.
2) Your model has 1 or more instances of ASF and no instances of ASL.
2a) If its target is not striking at the ASF step (ie is not in group 2 of this list), it strikes at the ASF step and gets rerolls if its Iniative is equal or higher to the target's.3) Your model has no instances of ASF and 1 or more instances of ASL. It will strike at the ASL step.
2b) If its target is striking at the ASF step, it then strikes simultaneously with its target and neither get rerolls from ASF, regardless of Initiative values.
4) Your model has 1 or more instances of ASF and 1 or more instances of ASL. The model is treated exactly the same as option 1 of this list. The "extra" isntances os ASF and ASL do not stack in any way and ASL specifically tells you that ASF and ASL cancel; in other words, the model is treated as though it has neither rule when it comes to the order of combat, ie. it strikes at Initiative and does not hamper opponent's rerolls if they happen to have ASF.
I will reiterate, ASF covers what to do with ASF in combat against targets with ASF and without ASF. ASL covers what to do in combat if you have ASL and specifically states that having both ASF and ASL causes the rules to negate each other. The FAQ addition of non-additivity of Special Rules closes any loophole arguments on have 2+ instances of ASF or ASL causing that rule to reign.
True, a properly cross-referencing rule set would have ASL mentioned in the ASF description, but it would technically be redundant, since if you have both rules you'd need to read both descriptions, so the overlap only needs to appear in the text of one of them.
1) Do you have one or more instance of ASF?
-Yes, go to step 2.2) Do you have one or more instance of ASL?
-No, go to step 3.
-Yes, go to result I.3) Do you have one or more instance of ASL?
-No, go to result F.
-Yes, go to result L.
-No, go to result I.
F) You strike at the ASF step, with all the perks that implies!
I) You strike in normal combat order (i.e. at Initiative). An opponent striking at the ASF step may get rerolls against you if its Initiative is equal or greater than yours.
L) You strike at the ASL step.
I can't make it any clearer than that other than to write out the full text of the relevant rules and how you properly cross-reference them.
P.S. For others following along who are wondering how SoA affects this, it's simple, pretend the ASL from the GW does not exist, then process as normal.