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Fixed enhancement bonuses do not stack with enhancement bonuses from magic items. So, you can keep the bonuses on magic items without any problems. This will help magic items retain some of their uniqueness and usefulness, since (for example) a +2 sword might be better than the party's current fixed bonus. It will also ensure that your players keep looking for new magic items, since that +2 bonus will eventually be overshadowed by the player's inherent bonus.

Boons, hirelings, henchmen, original items of your own design, recharging spent daily powers, story/character driven rewards, etc. There's plenty of things to use to reward players that does not involve a shiny new magic item. I've often found that my players take to the little things that affect their character personally better than to the things that affect their character's math. Your milage may vary on this one though, since there are some players driven by wealth and power in the math terms.

If you'd rather not hand out new items, decide ahead of time the items the a player really wants, work those in, and simply upgrade them as needed offscreen with levels. Every +1 sword of whatever-it-does need not always be a big deal that it gets it's own 5% cut of in game screentime  when you find it. Leave that for the fights where that sword will shine the most to begin with.

Happy Gaming

Nothing wrong with working in story awards. Keep inherent bonuses (gets rid of the required upgrades) Then have them quest for specific gear, maybe the fighter wants a Luckblade so he quests for it eventually finds it at the end of a quest and it's a +1 Luckblade. as the story goes on you can drop different story rewards in, one of the good deities helps the party out upgrading each of their gear so the fighter's luckblade gets enhanced to +2.

Talk with your players, let them know the type of campaign it will be, and have them tell you what items their characters want then build minor quests around that. The character playing the wizard wants a new staff? Perhaps the wizard has to hunt down his master who has been missing for 10 years because he knows the master has a staff like the one he wants. The rogue wants some magical boots? Well he knows a guy who knows a guy who knows a guy who heard of a guy who has a pair of those boots and he might be willing to trade for a favor or a price. The ranger gets a vision from a nature deity or a primal spirit showing the way to a mystical bow deep in the forest.

Another approach I've done in the past because I also get tired of the PCs needing to upgrade their equipment every few levels, is ignore the different types of magical equipment. What I mean by that is for example Holy Avenger. There is a Holy Avenger that floats about the multiverse. There's not a +5 Holy Avenger and then also a +6 Holy Avenger. There is just Holy Avenger. The level break downs of an item is what power capabilities a character of that level can unlock. I'll do a couple more examples. There is a set of Exalted Chainmail armor at level 1 it's an ornate set of masterworked chainmail armor, beautifully crafted and gives off a magical aura, but the character's aren't good enough to unlock it's enhancement bonus, (whether or not they can use the power is up to you) but when a character wearing the armor reaches level 5 it resonates with the character's power and grants the wearer the +1 enhancement bonus to AC. When the wearer reaches level 10 it resonates further granting a +2 enhancement bonus and so on and so forth for the description of the item. Usually I let the players use the powers of the equipment regardless of the levels so there is incentive to keep it over something else that may be a little better at lower levels.

This reduces the need to continually grant characters more and more magical items. A level 2 fighter does a quest and finds a flaming longsword. Right now the longsword will do fire damage and the character can use the daily power, but at the moment it does not have any enhancement bonus to attack until the character reaches level 5.

Just something I've one in the past like I said. The inherent bonuses balance out for the items they don't pick up (NADs bonuses and such) and it makes each and every magical item a momentous occasion without making them trivial, but as long as you let them quest for specific items they may want (Mostly for powers and such) then it allows them to continue to customize their characters. Just my 2 cp good luck and happy gaming.

You could also talk to the players and have their characters motivated by things other than swag.  If the character adventures because, say, he wants to protect innocents rather than get rich, the issue of 'rewards' goes away completely.

If you're using Inherent bonuses, the PCs don't have to upgrade their weapons every five levels, their Inherent bonus automatically goes up as they level, and when the Inherent bonus exceeds the Ehancement of their weapon/implement/armor/neck items, the Inherent bonus kicks in and raises thier relevant stat automatically.