I'm of the opinion that Heighten Spell is nearly worthless 95% of the time. So finding a way to make it more powerful is a good thing, but consider that the metamagic feats to both of your suggestions already exist as options in Enlarge Spell and Intensified Spell. Adding both to the Heighten Spell seems too strong to me.
Some people like to play where every spellcaster gets Heighten Spell for free.
Both of those grant a benefit at a cost of +1 spell level, but the increase in damage dice takes place 1 every two levels and I thought about granting an increase of one range category (e.g. touch to short) for every two levels as well. This would make the feats dedicated to those effects better, and still boost Heighten Spell to make it better reflect increasing the spell's level.
They don't cost a +1 spell level. They cost a +1 spell slot. While this seems like the same thing it isn't.
Enlarge is designed to increase the range of the spell to keep the caster safe from ranged attack.
Intensify is designed to allow you to increase the damage dice of a spell based on your caster level.
Heighten specifically increases a spells ability to punch through spell resistance and similar effects.
Each metamagic feat is designed to do one specific thing. By combining three feats; Enlarge, Intensify, and Heighten; you'll effectively break the metamagic feat system. Meta magic feats are designed to be used in concert with each other. With what you suggest you'd be allowing players to increase their damage; with intensify and heighten; as well as their range; with enlarge and heighten; on top of increasing the spells ability to punch through spell resistance.
Fireball; level 3 sorc and wiz spell dealing 10d6 (max 60 dmg) damage at caster level 10 and 400ft +40ft per level; could be changed into a 17d6 (max 102 dmg) damage with a range of 1600ft 160ft per level with the ability to break through spell resistance as if it were a 7th level spell.
Even if you don't intensify and enlarge it, that version of Heighten would cause it to do 13d6 (max 78 dmg) damage with a range of 1600ft + 160ft per level, and the spell resistance breaking power of a 9th level spell. Effectively making Enlarge Spell a completely useless feat to take.
In short, I wouldn't do it. It's way too easy to abuse and utterly breaks the system of Metamagic.