If you got the rat sputnik and tube it wouldn't cost too much, and keep her existing familiar toys too
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Rat rations sell the rat sputnik for £4.99 and you can choose your top and bottom colours
Sputnik - XL - £4.99 : ratRations.com
The tubes are a couple of pounds at Rat rations too
Chew Tubes - Boredom Breakers - £1.61 : ratRations.com
Generally rat sized toys and houses are good for Syrians
I tied mine up with sisal string - not easy to find but you can get it on ebay. Or there are other rat sized tubes you can get as well. If you like that idea. I'd avoid hammocks if she's a chewer.
Charlie loved his Sputnik and a lot of hams on here do - especially if you put substrate in it. He also had the small sputnik that came with the cage - I used to have that over his house roof and put his veggies in it.
But - it might be that she is just a real chewer and it could be better to put the money towards something like a Zoozone 2 instead and keep her existing toys. You can still have a sputnik in a Zoozone though.