Why would heavy armoured cavalry survive? The Welsh longbow would stop them as per Agincourt (at least in English military legend). It was seriously suggested in Napoleonic times that the longbow should be used rather than the musket, more efficient and faster rate of fire. No gunpowder might mean English ascendency at least for a time as the longbow was at least as good as the crossbow and easier to learn and use. Mind you apart from Henry V most of our military leaders at that time weren't that good!
You should really look up about what happened at Azencour and elsewhere.
The English were basically dug in to near-WW1 levels and also protected by heavily armoured men at arms, had the battleground of their choosing, were defending a hill, and had terrible French leadership play right into their aims. They were able to repeat this success with Scotland through to the 16th c. because Scotland if anything had an even more insane and antiquated martial traditions than France.
All other times and situations the longbow troops were slaughtered, sometimes in just minutes. This happened at Patay (knights ride down insufficiently dug in longbowmen arranged for battle in a line taking almost no losses), Formigny (longbowmen successfully defend camp against French foot until lured out into the open, ridden down very quickly by Breton cavalry), at Gerberoy (French men at arms and light horse surprise longbow and infantry column on the march and break into a half-complete fortified camp before reinforcements can link up).
Longbowmen, hired by their thousands, managed to have no positive impact in Charles of Burgudny's service. They were mildly effective but nothing special in Italy and Hungary either.
Longbows are a potent weapon when tactical setups are perfect and when they are supported by men at arms of their own. It's basically pretty clear from historical record that armoured cavalry outlasted the mass longbow fad everywhere including England proper.
Don't be getting flung off into the abyss, now. (Monty Python reference

)
Longer ranged and some more powerful than a javelin, I'll make a pitch for the Atlatl (spear thrower). Although the bow and arrow supplanted the atlatl in most cultures, it was in truth a device with a balance of range and power unique to itself. The primary disadvantage is it has a steeper learning curve than either bow or javelin.
Atlatls (or at least the unique Atlatl the Tarairu of the brazilian highlands used) were known to be able to pierce the armor the Portuguese were wearing in the 17th C:
(Must have been a uniquely hard wood to be able to go through metal!)
Prins, Harald E.L. (2010). The Atlatl as Combat Weapon in 17th-Century Amazonia
Did Harald Prins ever try to recreate this scenario with faithful modern replicas? Because until then this reference is worthless. I cannot emphasise this point enough.
What is "17th c. Portuguese armour" - harness? munitions breastplate? mail? brigandine? padded linen/cotton? A combination of the above? Was the person actually wearing it? Was it rusted? What was the range? Where did it hit? We don't know these things.
There's 17th c. Russian accounts saying the same thing, that "against the bows of the Siberians, neither mail nor brigandine can stand, it shoots clean through both sides". This is especially odd because the Russians themselves wore a variety of armour in their European wars and some 20+ % still used bows functionally identical to those used in Siberia (and the others used firearms! So you know, beating mail with ranged weapons should have been a regular occurrence to them). Why would people wear the stuff if it was useless? They would not, as is shown by rapid decline in armour once grapeshot and flintlocks appear.
And needless to say it hasn't been reproduced at all.
This is (as silly as it sounds) a very new field. People did not do much reconstruction work when interest resurfaced in the 19th c., and historical records aren't definitive without the level of detail and context that we simply do not have.