I definitely want to stay away from making it turn based. I think we should try to figure out how to make the battle screens work. I think it would work nicely. Leveling doesn't need to be complicated, but I think there should at least be some level of control over what areas your character excels in. So I think maybe we should outline all the skills that would be easy to implement in a top down 2D environment.
I'll make a list of levelable skills.
Speed - how fast the character runs, not very complicated. Possibly call the stat agility and have it also relate to how fast they can attack. Maybe after this skill levels enough the character gets a new ability such as rolling to avoid attacks. A possible option for stats is allowing the player to choose one special ability for the stat they train the most on.
Stealth - Higher stealth means longer before an enemy notices you when you get a surprise attack battle screen. It also gives you a better probability of picking a lock on a chest or a door (lock picks could be a single use item that either breaks or opens a lock. With higher stealth, you'd have a greater chance of picking a lock, and a lower chance of breaking your lock pick.) A special ability for stealth would be temporary invisibility or something.
Strength - how much damage the player does in battle. Pretty self explanatory. A special ability for strength would be a special strong attack which the player uses and then has to recharge.
Magic - how much mana the player has for magic abilities. Leveling this up would let you use a summoning spell to summon NPCs to fight for you as a special ability. As an added bonus, every magic level your maximum mana goes up by one, and your type of NPC that you spawn gets a bit better. The NPCs wouldn't be OP, just a little help in battle. You might also get faster mana regeneration with this stat.
Vitality - how much health the player has. Choosing to level this up the most gives the player a quick heal ability, using mana to heal instantly instead of using potions or other healing items.
Defense - counter damage to oncoming attacks. For example, say the enemy has an attack of 7 and you have a defense of 2, the enemy's attack would deal 5 damage. To prevent this from being super OP and keeping weak enemies from doing any damage at all, defense can only limit an enemy's attack to 1/3 of its original strength. The ability for this stat would be magical shield that deflects enemy projectiles and defends against melee attacks.
The player would get one special ability for his player, based on what stat he has most leveled up. The ability will change to always match the skill you have the highest level on. That way it's not a permanent decision and it allows the player to test them all out if they wish. You get a few upgrade points each time you level up, which you can apply to these skills.