Was it a mistake bringing this phone to Israel? - Galaxy S III Q&A, Help & Troubleshooting

This is a technical question and even though it's about the t-mobile t999 I decided to post it here as well because the post relates to the international version as well. Here it is:
I live in Israel. I used to live in the US. Last time I was in the US I bought this phone and brought it over. I did my research beforehand and knowingly purchased the phone assuming I would have full compatible with Israeli service providers...
Now, I'm not so sure anymore. I just tried the phone today.. maybe 5 hours of use. Still have the default OS installed. No root or anything. The signal seems to fluctuate going between Edge and higher speed networks.
Here's what it says about Cellcom on wikipedia:
Cellcom eventually sought to replace the 850 MHz TDMA frequencies it owns with standard 900 MHz GSM frequencies but Pelephone and Partner (Orange) petitioned the Ministry of Communications to deny this for technical reasons. This put Cellcom at a disadvantage since though most of its users had converted to GSM, they were not able to make use of the lower frequency's better in-building penetration and greater cell reach.
With its entry into 3G wireless services Cellcom demoed the first mobile video call in Israel. Since the beginning of 2006, Cellcom began deploying a 3G UMTS-2100 network nationwide which by the end of 2007 covered than 87% of the population. Cellcom was the first in Israel to launch an HSDPA network (also called "Generation 3.5") nationwide. In 2011, Cellcom began to deploy UMTS services in the 850 MHz band, employing unused capacity in that frequency range since it had very few TDMA customers remaining. The Israeli Ministry of Communications has approved Cellcom's plan to shut down the TDMA-850 network on 31 December 2011.
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It supports the following networks:
GSM, GPRS, EDGE, UMTS, HSDPA, SMS, MMS, iMode
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I just put the SIM card back in my old international Galaxy 2 i9100T and it'll fluctuate between HSDPA: 8 and HSPA+:15. Also it displays an H icon in the status bar (I don't think Resurrection rom is capable of displaying an H+).
Anyway, I'm going to put the SIM back in the Galaxy 3 t999. It now fluctuates between EDGE: 2, HSPAP: 15, HSPA: 11, and UMTS: 3. The signal is shifty and only displays a 3G at the top, no H like the international Galaxy 2.
Here's what wikipedia lists as the differences between the two models of the Galaxy 3 (standard international i9300 and my t-mobile t999):
Model GT-I9300;
2G networks: 850, 900, 1,800, 1,900 MHz GSM / GPRS / EDGE
3G networks: 850, 900, 1,900, 2,100 MHz UMTS / HSPA+
no 4G of course
max speed: 21 Mbit/s HSPA+
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and
Model SGH-T999;
2G networks: 850, 900, 1,800, 1,900 MHz GSM / GPRS / EDGE
3G networks: 850, 1,700 (AWS/Band IV), 1,900, 2,100 MHz UMTS / HSPA+ / DC-HSPA+
no 4G either
max speed: 42 Mbit/s DC-HSPA+
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and this is what gsmarena.com says about the cellular capabilities of Israel:
2G capabilities: Required GSM 900 Recommended GSM 900 and GSM 1800
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3G capabilities: Required UMTS 2100 Recommended UMTS 850 and UMTS 2100
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So what do you think is going on??? Doesn't the t-mobile Galaxy 3 t999 support all the networks that Israel currently has operating???

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It could be an OS issue. Have you tried flashing yet?

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You will never get an H or H+ with a T-Mobile branded GS3. It's as simple as looking at your User Manual.
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Your phone contains all the networks for Israel, but it's optimized for T-Mobile's network. So you aren't going to get the performance you would get with the International GSIII.