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This is a problem that many workers with injuries get themselves into with the EDD. The reason why your SDI claim held up your UI claim is that in order to receive and continue to receive unemployment benefits you need to be ready and able to work. If you are disabled, it means that you are not ready and able to work, so while you would be eligible for SDI, you then eliminate your UI eligibility.
At the same time, this is an automatic flag to the EDD that something may be amiss in your UI claim, since your SDI claim means that you're claiming that you actually weren't ready and available to work during the time you were collecting unemployment benefits. When you send in an SDI claim form after receiving UI benefits for a period of time, the EDD may call into question whether you were disabled and unavailable to work during the time you were receiving unemployment benefits.
Unfortunately, there is no way or unringing this bell once its been rung, but you can do your best to minimize the damage. If you want to continue receiving UI and have your SDI canceled, you should inform EDD that the doctor who treated you was in error and that you are available and able to work, especially considering you have a job offer coming in a month.
EDD may be skeptical of this, so if they don't take you at your word, you may need to get another doctor's opinion, or the same doctor's opinion to state that you are ready and available to work as you first stated.
A second option would involve an 'alternative fact pattern.' If you somehow aggravated your injury after work and before you saw the doctor. If that is the case, then your unemployment benefits claim could be considered valid as well as your new application for SDI benefits, since you would have been available and ready to work prior to the aggravation of your injury and unable to work afterwards.
I'm not advising you to be dishonest with the EDD, but the latter fact pattern is likely to lead to a better result (EDD allowing your prior UI claim and granting your SDI claim), although it may need to be supported by statements that you made (or didn't make) to the doctor when he filled out the SDI application for you.
I know the above can be a little confusing, so again, please let me know if you have any follow up questions or need any additional information.
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Thanks and best of luck!