The effect boxes almost certainly are affecting the impedance level combined with the padding of Tascam's High-Z guitar input making your signal strength "very thin."
Check with Tascam, who are good about responding on customer's issues; if I may emphasize, I would contact them before doing anything else in order to make sure not to damage the unit by trying to get around the issue--it can be overcame but let them provide details. You've got $500 plus in your 32 track unit: Don't be like me and think the problem is solved on paper only to damage equipment instead in application of a solution. I always contact any manufacturer on issues of potential ruin if not done correctly; I can say I have always been contacted back by email on an issue by any manufacturer.
On amp modeling (cabinet modeling as what you will find typically it designated in literature), you may want to consider a used Roland GR-55 guitar sythn unit, which has a vast array of cabinet and guitar modeling selections, all your effects, and, of course, you get a guitar sythn that has supreme instrument reproduction and opportunity to create unique effects. These run about $500 to $575 used, about $800 new--I see used ones in the aforementioned price range all the time on a major guitar retailer site. See several YouTube videos for effects as well as sythn capacity-not sure if there what there YouTubes are on cabinets and guitar modeling with GR-55 (never looked), but you can download the list of all presets from Roland. By the way, your Tascam has a guitar modeling library; not sure if cabinets, too. I have the DP24SD.
Of important note, the blue GR-55 had some issue when first issued; look for a black one. I was told this personally by a factory rep, who also said the issue had been resolved, which is fine if buying new. The used prices are the same, slightly more blue ones sold. Additionally, you'll need the GK-3 pickup that may or may not be sold with the used unit but is needed, or bought new for a couple hundred--I'd wait until found since people sale the GK-3 often with the units and the price isn't jacked, maybe $25 ($575, or less). (The GK-3 pickup and jack unit are easily mounted, see YouTube).
On amps, you may want to consider the legendary Pig Nose, which Clapton used on an album as have other major artists . . . oh, yes, the price for this small amp new is about $100 if including cord. Plays clean to dirty simply by volume control (combination of balancing guitar volume and amp level, if I understand correctly per desired sound), not built in effects (see YouTube on how to control tonal properties). It possibly might, not sure, be able to be used with effects, but the sound is so diverse you may dig its range of dynamics by itself.
About mics, while tonal quality is a personal taste, as I am someone on a progressing entry level, I have found that it is important for those beginning to learn of recording to know that the response signal is flat, meaning that no dips or peaks are unwantedly is occurring, unless intentionally for special application, like drum mic'ing. With a flat mic signal, if there is something that you are getting unexpectedly in certain ranges, you'll know it is not the mic beyond placement--remember, flat does not in any way mean boring--easily confused; it means the mic'ing response that a mic can achieve that is closest to recording what there is to hear.
Rode makes the NT1 condenser mic, which has a perfectly flat line 30Hz to 12K response with a gentle roll off; moreover, its self-noise is among lowest available: Used at $150-175, with needed shock mount to minimize vibration. In a world of a couple thousand dollar mics, this mic is extremely good for instruments or vocals--nothing close to it in specs for price. To contrast this point, I have a low-priced Marantz with a self-noise of 19dB as opposed to the 4.5 dB of the Rode NT1.
Beyerdynamic makes a $350 (approximate new price) dynamic mic with an equally flat signal as the Rode NT1 condenser. What is the difference? One of the major retailer's online has a well rounded collection of articles and glossary of technical terms. I am sure there are other resources similar; unfortunately, I am unsure if it is within forum protocol to mention retailers; however, since there are only a handful of major retailers online, if you would like to search for their collection it is called InSync. It has a lot of recording articles as well as other topics that are easy to understanding; it is meant to educate the consumer, so its level of communication is for entry to intermediate to sometimes advanced.
Don't ruin that Tascam, looking forward to hearing some joyful sounds.
By the way, a production company called ProAudio offers an instructional Tascam 32 DVD (not SD but usable for newer models); it can be purchased on Tascam's website, but found cheaper elsewhere. The sound engineer who had instructed on the DVD has worked with major talent; he has also produced a 3 DVD on recording and mixing--a bit expensive, but based on the content of the DP24 video, I am excited about getting into that material.
Respectfully, JeffF.